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Answer: Clearly the most important beracha of Havdala is the final one of Hamavdil, which contains its basic content. The berachot on besamim and on fire are not crucial obligations (Shulchan Aruch, Orach Chayim 297:1; ibid. 298:1), and while they are preferably attached to Havdala, they can be said at other times as well (Rama, Orach Chayim 298:1). Thus, if one did not hear those berachot, it does not affect Havdala (Mishna Berura 298:3), but he should make the berachot when he is able to during the course of the night.
In contrast, the cup of wine that one uses for Havdala is part and parcel of the mitzva on a Rabbinic level. Realize that normally we have already fulfilled the Torah-level mitzva of Havdala previously, during Ma’ariv. We recite Havdala again in order that the second time it will be with wine. In your case, on the one hand, you heard the beracha of Havdala recited by one holding a cup of wine. On the other hand, you did not hear the beracha of Borei Pri Hagafen on that wine. Is that lacking enough to prevent you from fulfilling the mitzva of Havdala?
The Magen Avraham (296:10; see Pri Megadim ad loc.) discusses one who heard a complete Havdala but had in mind to include himself in the beracha of Hamavdil but not of Borei Pri Hagafen. He says that such a person fulfilled the mitzva of Havdala, just that he cannot drink the Havdala wine without making a new beracha. The Mishna Berura (296:33) explains that whereas Hamavdil is the essential beracha of Havdala, Borei Pri Hagafen is needed only to enable one to drink the wine.
Several Acharonim (including Shulchan Aruch Harav, OC 172:(2); Igrot Moshe, OC III:45; Chelkat Yaakov I:91) demonstrate the extent of this distinction’s cogency by comparing the beracha structure to that of the parallel mitzva of a holy declaration performed on Shabbat over a cup of wine – Kiddush. The Shulchan Aruch (OC 271:4) posits that one who was in the midst of a meal in which he had already made a beracha on wine when Shabbat began makes Kiddush without reciting Borei Pri Hagafen. Admittedly, regarding Havdala during seuda shlishit that included wine, there are two opinions in the Shulchan Aruch (OC 299:3) whether one recites Borei Pri Hagafen. However, the stronger opinion is that he does not need to (see Mishna Berura ad loc. 10). In any case the issue is whether Havdala is considered part of the meal (ibid.), and not whether Havdala counts without Borei Pri Hagafen, which it clearly does.
Your case, when Borei Pri Hagafen was said but you did not hear it, is no worse. There is even a question whether Borei Pri Hagafen is crucial for the one who makes Havdala and is not in the midst of the meal. Rav Moshe Feinstein (ibid.), based on the rule learned from the aforementioned Shulchan Aruch that the beracha is only important to allow one to drink, posits that if one mistakenly recited Shehakol on Havdala wine, he fulfills Havdala, as he is able to drink. He further proposes that even if one forgot to make any beracha but already drank the Havdala wine, he fulfilled the mitzva. (If one did not drink a sufficient amount of wine, there is uncertainty about whether he has fulfilled Havdala (see Shulchan Aruch Harav, OC 190:4; Shemirat Shabbat K’hilchata 30:36)).
Shemirat Shabbat K’hilchata (vol. III, notes to 60:(91)) cites Rav Auerbach as saying that since one needs to drink the wine and needs the beracha for that, Borei Pri Hagafen is a part of Havdala that listeners need to take seriously. However, concerning after the fact for one who missed it, Shemirat Shabbat K’hilchata (60:30) agrees that there is no need to hear Havdala again, and he cites several poskim who agree. This covers cases of one who came in after Borei Pri Hagafen was said, or he did not hear it or concentrate on it. While you would have needed a beracha before drinking the wine, there was, of course, no need for you to do so.
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