Saying Aleinu Leshabeiach together with the congregation:
When the congregation recites Aleinu Leshabeiach, one is to say it together with them. This applies even if one has already Davened, and just happened to walk into Shul at the time the congregation is reciting Aleinu. It likewise applies if he was already in Shul and is in the midst of reciting supplications or verses, in an area that it is permitted for him to stop.
Past Baruch Sheamar: If one is in the midst of Davening, past Baruch Sheamar, he is not to recite Aleinu together with the congregation. [Nevertheless, he is to stand up and bow upon the congregation reciting the words of “Veanachnu Korim”, as explained next.]
Bowing together with the congregation: If for whatever reason one is not reciting Aleinu Leshabeiach together with the congregation [such as if he is in an area of Davening in which an interruption may not be made, as stated above] he is nevertheless to [stand up and] bow, upon the congregation reciting the words of “Veanachnu Korim”.
If one is after Shemoneh Esrei, prior to Aleinu, and the congregation has already reached Aleinu Leshabeiach, is he to stop in middle and recite Aleinu together with the congregation?
Ø Example: One is in the midst of Uva Letziyon and the congregation is saying Aleinu, must he stop and say Aleinu together with the congregation? This can occur in the event that the Chazan is Davening a quicker pace than oneself, or if one finished Shemoneh Esrei later than the congregation, or one is Davening in a Nussach Ashkenaz Shul which recites Aleinu immediately after Uva Letziyon.
Some write he is not required to stop and recite Aleinu with the congregation, although he is to bow upon the words of Veanachnu Korim being said. Others write he is to say Aleinu together with the congregation, and then repeat it again at the end of his Davening. Practically, the Rebbe’s directive follows the latter approach, to stop and say the entire Aleinu with the congregation, and then repeat it again in its entirety at the conclusion of Davening.
After Shemoneh Esrei, before Tachanun: If one has finished Shemoneh Esrei and is holding prior to Tachanun, he is not to stop to recite Aleinu Leshabeiach, and is rather to go straight to Tachanun. [However, he is nevertheless to bow upon the words Veanachnu Korim are being said, as stated above.]
If one is in the midst of learning Torah, must he stop to recite Aleinu Leshabeiach with the congregation?
Some Poskim write he is not required to do so, although nevertheless he is to bow upon the words of Veanachnu Korim being said, as stated above.
 Admur 65:2 regarding Shema, Ashreiy and “the same applies to any other matter that the congregation is reciting, one is to read together with the congregation due to Derech Eretz”; M”A 65:3; Shivlei Haleket 44; Elya Raba 65:2 and 237:4; Soles Belula 65:3; Chesed Lealafim 65:2; Machatzis Hashekel 65:3 “The same applies for Aleinu Leshabeiach”; M”B 65:9 “such as Tehila Ledavid or Aleinu”; Ketzos Hashulchan 13:6; Kaf Hachaim 65:4
Background: This concept of saying Aleinu together with the congregation is not explicitly mentioned in earlier Poskim, prior to the Machatzis Hashekel, although is self-understood from the wording of Admur and M”A ibid which state “any other matter”. Vetzaruch Iyun if this would include other paragraphs that the congregation states aloud throughout Davening. Seemingly however it does not include parts of Davening which the congregation recites silently, as otherwise the entire Davening would be included in this precept. Likewise, if it is recited quietly, there is no noticeable lack of Derech Eretz if one recites a different psalm during that time. See Piskeiy Teshuvos 66:3 and the Poskim in footnote 26!
Is this an obligation? Some Poskim explain that the above requirement to say Aleinu and Ashreiy together with the congregation is not an obligation, as is the recital of Shema, and rather is merely a proper act to perform, just as the Michaber 65:3 rules regarding reading the rest of Shema together with the congregation. [Mamar Mordechai 65:6; implication of Elya Raba ibid; Kaf Hachaim ibid]
 The reason: As one is required to join the congregation upon them reciting a prayer [in unison] as a sign of Derech Eretz, proper conduct. [Admur ibid]
 Admur ibid regarding Shema “One who read Shema and entered into the Shul and found the congregation reciting Shema…and the same applies to any other matter that the congregation is reciting.”
 Admur ibid; Michaber 65:3 regarding Shema
 1st opinion in Admur ibid [and Michaber 65:2] regarding Shema, Ashrei and other matters the congregation is reciting; Ketzos Hashulchan 24:11; Minchas Yitzchak 9:8
Background: Admur ibid states regarding Shema, Ashrei and other matters the congregation is reciting “If he is in the midst of an area that he is not allowed to stop, such as from Baruch Sheamar and onwards, then he is not to stop…” Now, although Admur ibid brings two other opinions in this matter, and the final ruling is that one may recite the first sentence of Shema in the midst of Pesukei Dezimra, nevertheless, seemingly this only applies to Shema, as it involves Kabalas Ol Malchus Shamayim. However, other parts of prayer that one says with the congregation, one is to be stringent like the first opinion. [So is implied from the fact Admur records this dispute only regarding the first verse of Shema. See Mamar Mordechai 65:6; Elya Raba ibid; Kaf Hachaim ibid who state that these verses have the same status as the rest Shema and not as the first verse of Shema; So is also implied from Ketzos Hashulchan 24:11 which states “One who is not reciting Aleinu Leshabeiach, such as he is in the midst of Pesukei Dezimra”; So explicitly rules Minchas Yitzchak 9:8 that one does not stop at all for Aleinu if he in an area that he is not allowed to interrupt.]
 Admur 109:2; Shlah Inyanei Tefila in name of Maharash of Lublin; Elya Raba 51:8; Ketzos Hashulchan 24:11
 Piskeiy Teshuvos 132:7
 Tefila Kehilchasa 17 footnote 31 in name of Rav Fisher; Vayeishev Hayam 5; Birchos Shamayin 1:27; See also Divreiy Moshe 1:35; See Mamar Mordechai 65:6 and Kaf Hachaim 65:4 that saying Aleinu with the congregation is not an obligation but merely a good act.
 Implication Admur ibid “It likewise applies if he was already in Shul and is in the midst of reciting supplications or verses, in an area that it is permitted for him to stop.”; Letter of Rebbe printed in Shulchan Menachem 1:272 in reply to what to do if one is Davening by a Nussach Ashkenaz Minyan “Say Aleinu at the end of the prayer, as writes the Arizal, and also join the Minyan and say it when they do. Both times you should say the entire Aleinu.”; See also Igros Kodesh 19:430 that if one is praying in a Shul that says Ledavid after Aleinu he is to say Aleinu with the congregation and then say with them Ledavid; Tefila Kehilchasa 17 footnote 31; See Kaneh Bosem 2:8 which seems to learn one is to stop
 See previous footnote
 Kaneh Bosem 2:8; Piskeiy Teshuvos 131:2
 The reason: As one is not allowed to make a long interval between Shemoneh Esrei and Tachanun. [Admur 131:1]
 Piskeiy Teshuvos 132 footnote 30; See Mamar Mordechai 65:6 and Kaf Hachaim 65:4 that saying Aleinu with the congregation is not an obligation but merely a good act.