One who was already Yotzei, or is not currently being Yotzei, the Mitzvah:^[1]

A person who already fulfilled his obligation of a Mitzvah, [or did not yet fulfill his obligation, but plans to only do so later on^[2]] may fulfill that Mitzvah on behalf of another who is equally obligated in that Mitzvah, to be Motzi him [i.e. blowing Shofar, read Megillah ].^[3] Nevertheless, regarding the blessing of the Mitzvah [i.e. Asher Kiddishanu, Kiddush, Havdala], one who has already fulfilled his obligation of the Mitzvah [or did not yet fulfill his obligation, but plans to only do so later on^[4]] may only recite the blessing on behalf of another if that person is unable to recite the blessing himself.^[5] If, however, the other person knows how to recite the blessings, then he is to recite it himself rather than hear the blessings from the person who already fulfilled his obligation [or does not plan to currently do so].^[6] [All this is Lechatchila, however, Bedieved, if the person doing the Mitzvah for the other also recited the blessings rather than the listener, nevertheless the listener fulfills his obligation of reciting the blessings.^[7]]

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[1] See for general rule: Admur 167:23; Terumas Hadeshen 140; See regarding Tzitzis: Admur 8:11; M”A 8:8; P”M 8 A”A 8; Tehila Ledavid 8:3; Kaf Hachaim 8:21; So rule regarding Kiddush: Admur  269:3; 271:4; 273:6; Michaber 273:4; M”B 273:17 Ketzos Hashulchan 81:4; 96:5; Kitzur Halachos Shabbos p. 114 and 164, 273:42 footnote 69; 296 footnote 32; SSH”K 51:1; Piskeiy Teshuvos 273:5; Koveitz Hearos Ubiurim Tzemach Tzedek 7:87; Hearos Ubiurim Ohalei Torah 1024 p. 56; 1025 p. 65; 1026 p. 74; 1028 p. 79; So rule regarding Havdala: Admur 296:17; 297:8; Kuntrus Achron 272:2; So rule regarding Shofar: Admur 585:5; M”A 585:3 based on Terumas Hadeshen 140; Opinion in M”B 585:5; Machatzis Hashekel 585; P”M 585 A”A 3; Derech Hachaim 2 regarding Shofar; Mateh Efraim 585:6; Chayeh Adam 141:7; Kaf Hachaim 585:21; So rule regarding Chanukah: P”M 676 A”A 4; Ben Ish Chaiy Vayeishev 6; Kaf Hachaim 675:9; [See however M”A 676:4 in name of Hagahos Maimanis and Kaf Hachaim 676:13 that one person can light and another can say the blessing, and they do not state that it’s better for the person to say the blessing rather than the emissary.] So rule regarding Megillah: Opinion in M”B 692:10; Kaf Hachaim 692:14 and 25; See Derech HaChaim 3; Minchas Yitzchak 3:53-54; Salmas Chaim 269; Luach Tukichinsky; Kinyan Torah 3:103; See Sdei Chemed R”R 2:19; Piskeiy Teshuvos 692:7 that so is custom today

Background: The Rama 585:2 rules that the blower is to recite both blessings whether he is blowing for himself, to fulfill his personal obligation, or whether he is blowing for others. The M”A 585:3 brings the Terumas Hadeshen [140] who 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. Regarding Shehechiyanu the Terumas Hadeshen does not discuss who is to recite it. The Rambam, Mateh Moshe, Mahriv and Hagahos Maimanis rule that the listener is to recite it while the Beis Yosef writes that the custom is for the blower to recite it. It is based on these two customs written in the Terumas Hadeshen and Beis Yosef that the Rama here writes that the blower is to recite both blessings. Nevertheless 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 here follows the ruling of the M”A ibid.

Other opinions: Some Poskim rule the person may always say a blessing for the other even if he knows how to recite the blessing. [Rama 585:2 regarding Shofar; Michaber 692:3; Beis Yosef 585 that so is custom; Elya Raba brought in Kaf Hachaim ibid; See also Rama 671:7; M”A 671:11; Kaf Hachaim 676:13 who implies the person saying the blessing is to always be the person lighting]

Ruling of the M”B: The M”B 585:5 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.

[2] See Admur 273:6

[3] See regarding Shofar: Admur 591:1; Michaber 591:1; M”B 594:1; Kaf Hachaim 589:1; See regarding Kiddush, Megillah: Poskim ibid

[4] See Admur 273:6; Thus, if one is blowing for other Jews prior to Shacharis and he plans to fulfill the Mitzvah during Davening, the listeners are to recite the blessings if they have knowledge in how to do so.

[5] The reason it is allowed in such a case: Although the person who is saying the blessing is not fulfilling the Mitzvah at the moment, and hence does not need the blessing, nevertheless since all the Jewish people are guarantors to each other, therefore it ends up that he too needs this blessing now [due to his obligation of a guarantor]. (It is for this reason that it is accustomed for the Chazan to recite the blessing [over Tzitzis] aloud in order to fulfill the obligation of one who is not an expert.) This same law applies by the blessings of all Mitzvos. [Admur ibid]

[6] 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 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.]  

[7] Admur 273:6; Terumos Hadeshen 140