The Halachic authorities address an interesting question that arises in a case where a person did not recite Minha on December 3rd, the day before we begin reciting "Barech Alenu" in the Amida in place of "Barechenu." As we know, if a person forgot to recite Minha, or if he was unable to do so due to circumstances beyond his control, he has the opportunity to make up the missed prayer by reciting an extra Amida at Arbit that night. In the case of one who forgot to recite Minha on December 3rd, he would recite "Barech Alenu" in both Amida prayers he recites that night at Arbit. Even though the prayer he missed was one which required "Barechenu," he would nevertheless recite "Barech Alenu" in both prayers, since he recites them in the period requiring "Barech Alenu." Even in the second Amida – which is the one recited to make up the missed Minha prayer – he would recite "Barech Alenu," and not "Barechenu."
If, however, a person in this situation mistakenly recited "Barechenu" instead of "Barech Alenu" in the second Amida, he has nevertheless fulfilled his obligation. Even though he was to have recited "Barech Alenu," he does not need to recite another Amida, since, after all, the Amida served to make up the Minha prayer, which required "Barechenu." This is the ruling accepted by Hacham David Yosef, in his Halacha Berura (vol. 6, p. 57; listen to audio recording for precise citation).
Some questioned this Halacha in light of the comments of the Magen Abraham (Rabbi Abraham Gombiner, Poland, 1637-1683) concerning the case of one who forgot to recite Arbit on the night of Rosh Hodesh. Of course, Halacha requires such a person to recite an additional Amida at Shaharit the next morning, and he must insert Ya’aleh Ve’yabo in both Amida prayers. The Magen Abraham writes that if a person in this case forgets to add Ya’aleh Ve’yabo in the second Amida, which is recited to make up the missed Arbit prayer, he must repeat the Amida. Even though one who mistakenly omits Ya’aleh Ve’aybo during Arbit on Rosh Hodesh does not repeat the Amida, one who omits Ya’aleh Ve’yabo in the extra Amida recited to make up a missed Arbit must repeat the Amida. This is the ruling of the Magen Abraham.
It is unclear whether Halacha accepts this ruling, but, in any event, the question arises as to whether this position can be reconciled with the Halacha mentioned above, concerning one who forgot to recite Minha on December 3rd. If we apply the Magen Abraham’s rationale to this case, we should seemingly conclude that the individual who mistakenly recited "Barechenu" in the second Amida at Arbit should repeat the Amida. Even though that Amida is recited in lieu of Minha, which did not require "Barech Alenu," nevertheless, it would seem that the Magen Abraham would require the individual to repeat the Amida – just as one must repeat the Amida on Rosh Hodesh morning in the case described above.
The answer, however, is that a clear distinction exists between the two cases. In the situation of Rosh Hodesh, Halacha indeed requires one to recite Ya’aleh Ve’yabo during Arbit; although Be’di’abad (after the fact), if one mistakenly omitted Ya’aleh Ve’yabo, he does not repeat the Amida, he is nevertheless required to add this insertion in the first place. Therefore, if one forgets Ya’aleh Ve’yabo in the "make up" Amida the next morning, he must repeat the Amida. When it comes to "Barech Alenu," however, this recitation is not required at all at Minha on December 3rd, and we may therefore be lenient in a case where one mistakenly recited "Barechenu" during the "make up" prayer at Arbit.
Summary: One who forgot to recite Minha on December 3rd, and must therefore recite an extra Amida at Arbit that night, recites "Barech Alenu" even in the extra Amida recited in lieu of the missed Minha. If, however, he mistakenly recited "Barechenu" in that Amida, he does not repeat the Amida.
