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Reading the Megillah on behalf of others: 
*This Halacha pertains only to laws involving one who is reading for a congregation after already fulfilling his obligation. For the general laws of hearing Megillah from a reader-See Halacha 3!
One who already heard the Megillah may still read the Megillah on behalf of others who did not yet fulfill the Mitzvah.
Who says the blessings? The reader may say [all] the blessings on behalf of others even if he already heard the Megillah reading and fulfilled his obligation. Nevertheless if the person who is listening to the reading is able to say the blessings himself/herself then the listener is to say the blessing and not the reader. [This law likewise applies if the reader did not yet fulfill his obligation, but plans to only do so with a later reading. Bedieved if the reader recited the blessings rather than the listener, the listener fulfill their obligation of reciting the blessings even in such a case.]
Having intent to fulfill the obligation: The person which is saying the blessings must have in mind to fulfill the obligation of the congregation. See Halacha 3 for further details on this subject!
Is a Minyan required? One may read the Megillah for others even if a Minyan is not present. [See Halacha 6B for the full details of this subject!] However the blessing of Harav Es Riveinu is only recited if there is a Minyan present. [See Halacha 10 for the full details of this subject!]
A women’s Megillah reading:
It is customary in many communities to have a separate Megillah reading for woman who are unable to attend the Shul’s Megillah reading. The following are the laws that relate to this reading.
Is the reader to fulfill his obligation with this reading? The person reading the Megillah for women is to first fulfill his obligation with the Shul reading. Alternatively he may read for women with intent to not fulfill his obligation and later on hear the reading in Shul.
Who says the blessings? When reading the Megillah for only women, and the reader fulfilled, or plans to fulfill, his obligation at another reading, then the women listening to the reading are to say the blessings themselves. [Each woman is to say the blessing to herself prior to the reading, or have one woman say it aloud for everyone to hear and fulfill their obligation.] If however the women listeners are unable to recite the blessing, the Baal Korei is to recite the blessing on their behalf.
The Nussach of the blessing: By a reading in which only women are fulfilling their obligation, the wording of the first blessing is .לשמוע מגילה This applies even in a case that the reader is reciting the blessings on behalf of the women. See Halacha 10 for the full details of this subject!
The after blessing: The after blessing of Harav Es Riveinu is not recited when reading for less than a Minyan of women. If there is a Minyan of women listening to the reading-See Halacha 10 in Q&A!
A woman’s reading: Each woman is to say the blessing to herself prior to the reading, or have one woman say it aloud for everyone to hear and fulfill their obligation. If the women are unable to recite the blessing, the Baal Korei may do so for them.
When reading Megillah for others who know to say the blessing should each listener say the blessing themselves or should one say it on behalf of them all?
If there are less than ten people present then each person is to say the blessing to themselves prior to the reading. If there are ten people present then one person says it aloud for everyone to hear and fulfill their obligation. However some rule that when reading for a group of women then every women is to say the blessing to herself even if there are ten women present.
May the reader have someone else take him over in middle of the reading of the Megillah?
Some Poskim rule that if a new reader is taking over, he is to restart the reading from the beginning. Others however rule that second reader is to continue from where the first reader left off. Practically one is not to restart the reading and is rather to continue from the area that the first reader ended. However some conclude that if it is not a great trouble to restart the reading, such as if only a few lines were read, then one is to do so. Likewise if the congregation agrees to restart from the beginning one is to do so.
May one who did not hear the reading of the first reader, take him over in middle? Yes. He is to continue the reading from where the first reader left off. This applies whether the second reader has already heard the reading or not. If however he has not yet heard the reading then he is to read the entire Megillah to himself with a blessing after he concludes the reading for the congregation.
If a child did not yet hear Megillah is one to repeat the reading for him?
If the child has reached the age of Chinuch then the reading is to be repeated on his behalf. This applies even if one assesses that he may not focus throughout the entire reading. Nevertheless in such a case a blessing is not to be recited.
May a child who already fulfilled his obligation read the Megillah for a child?
May a woman who already fulfilled her obligation read the Megillah for a female child or woman?
 Reading for women and children: Some opinions rule that a man that already fulfilled his obligation cannot read on behalf of women or children as they are not included within Areivus. [Degul Merivava 271; Tzlach Brachos 20b; Yeshuos Yaakov 186] Practically we do not rule like this opinion. [Shut Rav Akiva Eiger 7 and glosses on SH”A 271; Chasam Sofer 271; Rosh Yosef Brachos ibid; Avnei Nezer 439; Shaar Hatziyon 271/9; Minchas Yitzchak 3/54; Har Tzvi 2/122]
The Michaber ibid rules that the reader is to recite the blessings. This is similar to the ruling of the Rama in 585/2 regarding blowing Shofar for others. The M”A there [585/3] brings the Terumas Hadeshen  which rules that it is always better for the listener to recite the blessing, although he concludes that the custom is that the blower recites it. The M”A ibid concludes that this custom only applies if the listener does not know how to recite the blessing however if the listener knows how to recite it, then he is to do so, and he then fulfills his obligation according to all. The ruling of Admur below follows the ruling of the M”A ibid.
 This includes the blessing of Shehechiyanu. [Mamar Mordechai 692/6; Kaf Hachaim 692/25; Beis Yosef 585; Rama 585/2 regarding Shofar; Admur 585/5 regarding Shofar –“Both blessings”; Biur Halacha 641 “Leatzmo”; Chasam Sofer 143; Minchas Yitzchak 8/63; Piskeiy Teshuvos 692/7]
Other Opinions: Some Poskim write one may never recite the blessing of Shehechiyanu on behalf of another. [Beir Heiytiv 692/20 as rules Rambam Brachos 11/10; Mateh Moshe, Mahriv and Hagahos Maimanis] Practically we do not follow this opinion.
 Michaber ibid; Rama 585/2 regarding Shofar
 Kaf Hachaim 692/14 and 25; Opinion in M”B 692/10; Derech HaChaim 3; Michaber 273/4 regarding Kiddush; M”A 585/3 based on Terumas Hadeshen 140; Admur 585/5 regarding Shofar and 273/6 regarding Kiddush; Machatzis Hashekel 585; P”M 585 A”A 3; Derech Hachaim 2 regarding Shofar; Mateh Efraim 585/6; Chayeh Adam 141/7; Minchas Yitzchak 3/53-54; Salmas Chaim 269; Luach Tukichinsky; Kinyan Torah 3/103; Piskeiy Teshuvos 692/7 that so is custom today; See Sdei Chemed R”R 2/19
The reason: This follows the general rule that the blessings are to be recited by one who is currently fulfilling his obligation of the Mitzvah. [273/6] The Terumas Hadeshen 140 explains [regarding Shofar and the same would apply here to Megillah] that since the Mitzvah is to hear the sound of the Shofar and both the blower and listener are equally fulfilling this action of hearing, therefore it is better for the listener to recite the blessing, since he is fulfilling his obligation with the hearing. [This is unlike the law of placing a Mezuzah for another person in which case the person placing the Mezuzah says the blessing, as in that case he is the only person doing the action as opposed to the owner of the house.]
Ruling of the M”B: The M”B 692/10 records a dispute regarding this matter and concludes that many are accustomed to be lenient to always have the reader say the blessings. In 585/5 regarding Shofar the M”B rules that the custom is to be lenient and one is not to protest their opinion as so is the main opinion. The Kaf Hachaim 585/21 questions this ruling of the M”B as majority of Poskim ibid rule that it is to initially be said by the listener. However see Minchas Yitzchak ibid that explains the M”B did not mean to say that most Poskim initially rule this way.
 See 273/6; Thus if one is reading for women prior to Shacharis and he plans to fulfill the Mitzvah during Davening in Shul, the listeners are to recite the blessings if they have knowledge in how to do so.
 273/6; Terumos Hadeshen 140
 Meaning that only women are fulfilling their obligation with this reading.
 See M”A 689/1; M”B 689/1; Tosafus Eiruchin 3a that in previous times the men used to read the Megillah for their household. [Kaf Hachaim 689/3]
 The reason: As it is a Mitzvah for him to hear the reading together with the congregation in Shul. [M”A 692/5; M”B 692/11; See Halacha 7!]
 P”M 692 A”A 5; M”B 692/11
 See the previous part of this Halacha and the sources mentioned there
 As is the law by men, as explained in Poskim brought above. An additional reason mentioned is because according to some opinions men do not have Areivus for women and are hence unable to fulfill their obligation for them. [Minchas Yitzchak 3/53-54; Salmas Chaim 269]
Other Opinions: Some opinions rule that when reading for women the reader is to always say the blessing even if the woman knows how to say the blessing herself. [Kitzur SH”A 141/16]
 See Q&A!
 See Halacha 10 and sources mentioned there!
 M”A 692/5; M”B 692/11
 Mateh Efraim 585/6; Minchas Yitzchak 3/53-54
The reason for this is because it is to suspect for the opinion of the Michaber 689/5 that rules each person is to read the Megillah to themselves if a Minyan is not present. Hence although we are lenient regarding the reading of the Megillah, nevertheless we are stringent regarding the blessing. [Minchas Yitzchak ibid]
 Mateh Efraim 585/6; Salmas Chaim 269
The reason for this is because we assume that when there is a group of ten people there are bound to be some that do not know the blessings and hence one is to say the blessing for all, just like is always the law by a congregational reading. [Mateh Efraim ibid]
 Minchas Yitzchak 3/53-54 based on Shaar Hatziyon 689/15 in name of Karban Nesanel and Tosafus
The reason: It is to suspect for the opinion of the Michaber 689/5 that rules each person is to read the Megillah to themselves if a Minyan is not present, and that women do not join a Minyan. Hence although we are lenient regarding the reading of the Megillah, nevertheless we are stringent regarding the blessing. [Minchas Yitzchak ibid]
 M”A 692/2
The reason: This follows the ruling regarding Haftorah that the second reader must restart the Haftorah [Admur 284/10] and regarding Kerias Hatorah that the second reader must restart from the beginning of that Aliyah. [Michaber 140/1]
 Elya Raba 692/3; Shvus Yaakov 1/42; Chayeh Adam 154/26; Diggul Merivava
 The reason: As repeating from the beginning is a tremendous Tircha Detzibura. [ibid]
 M”B 692/2
 Shaareiy Teshuvah 692/1; Kaf Hachaim 692/11
 Kaf Hachaim ibid
 Shaar Efraim 6/60; Kaf Hachaim 692/12
 Piskeiy Teshuvos 689 footnote 36
 Who says the blessing? If the child knows how to say the blessing then this follows the same ruling as any time one is reading for another, in which case the person fulfilling the Mitzvah is to say the blessing .
If the child does not know how to say the blessing: The P”M 589 A”A 4 writes by Shofar that the adult may say the blessing on behalf of the child since he is obligated in Mitzvos, however he concludes with a Tzaruch Iyun. The Piskeiy Teshuvos 589/2 writes based on this that the adult is not to say the blessing.
 As it is questionable whether a child is included within Areivus and thus perhaps he does not have the ability to fulfill another’s obligation once he already fulfilled his own obligation. [P”M 689 A”A 4; Biur Halacha 689 “Venashim”] Regarding a child reading on behalf of a woman, even if he did not yet fulfill his obligation-see Halacha 4 in Q&A!
 As it is questionable whether a woman is included within Areivus and thus perhaps she does not have the ability to fulfill another’s obligation once she already fulfilled her own obligation. [P”M 689 A”A 4; Biur Halacha 689 “Venashim”] Regarding a woman reading on behalf of male children even she did not yet fulfill her obligation-see Halacha 4 in Q&A!