If one entered in middle of Havdala is he Yotzei?

Missed Hinei Keil Yeshuasi:[1] The saying of “Hinei Keil Yeshuasi” is a custom and not required from the letter of the law as part of the Nussach of Havdalah.  Accordingly, one who walked late into Havdalah and missed the saying of Hinei Keil Yeshuasi, nevertheless fulfills his obligation

Missed the blessing of Hagafen:[2] The lack of the blessing of Hagafen does not invalidate the fulfillment of Havdalah, and thus if the person saying Havdalah forgot to recite the blessing of Hagafen, and remembered only after finishing to drink, he nevertheless fulfills his obligation. Accordingly, one who walked late into Havdalah and missed the blessing of Hagafen, nevertheless fulfills his obligation so long as he heard the blessing of Hamavdil, as explained next. The same applies if he was in the room but could not physically hear the blessing of Hagafen, nevertheless he fulfills his obligation if he heard the later blessing of Hamavdil.

Missed Besamim or Haeish:[3] The lack of the blessings over Besamim and Haeish do not invalidate the fulfillment of Havdalah, so long as he heard the entire blessing of Hamavdil as explained next. In such a case that one did not hear/say the blessing over Besamim/Haeish, he is to say the blessing of afterwards.

Entered in middle of the blessing of Hamvdil:[4] One does not fulfill his obligation with any blessing unless he hears the entire[5] blessing [of Hamavdil] from beginning to end. Furthermore, if one did not hear the [entire] blessing then if he intends to fulfill his obligation with this blessing he may not answer Amen [and does not fulfill his obligation.[6]

__________________________________________________________________

[1] See Admur 296:3

[2] Admur 296:18 in parentheses “And even if he did not hear at all the blessing over the wine, he is Yotzei”; Kuntrus Achron 272:2 “It is incorrect to say that every Kos Shel Bracha requires a blessing of Hagafen…as in truth a Kos Shel Bracha is not dependent at all on the blessing of Borei Peri Hagafen as we see from the fact one can make Kiddush in middle of a meal without saying the blessing of Hagafen.”; Kuntrus Achron 299:3 “It is proper to say Havdalah without a blessing of Hagafen and be Yotzei Havdalah according to all, as blessings do not invalidate the Mitzvah.”, brought in Tehila Ledavid 271:18

Other opinions: Some Poskim rule that a Kos Shel Bracha requires the blessing of Hagafen recited over it for the sake of fulfilling the Mitzvah, and therefore one who does not drink wine cannot fulfill the Mitzvah of Kos Shel Bracha even if another person says the blessing over it. [Chacham Tzvi 168, brought in Admur 190:4, Kuntrus Achron 272:2, Tehila Ledavid 271:18] This implies that if the blessing of Hagafen was skipped, or missed by a listener, that he does not fulfill his obligation. [Tehila Ledavid ibid] 

[3] See Admur 298:3

[4] Admur 213:4 “From beginning until the end”; See also Admur 183:10; 193:1; Michaber 213:3; Rambam Brachos 1:11; Teshuvas Harambam Pear Hador 101; Brachos 53b; Yerushalmi Brachos 8:5; Megillah 1:9; Sefer Hamichtam and Hashlama ibid; Ravya 153 and 159; Peri Chadash 124; P”M 124 M”Z 4; Rav Elyashiv, brought in Maor Hashabbos 4 that must hear both beginning and ending blessing; See Piskeiy Teshuvos 296:4 footnote 31 for a discussion in Poskim in whether the beginning of the blessing is needed to be heard even Bedieved

Other opinions: Some Poskim rule one fulfills his obligation if he answers Amen to a blessing, and he knows the identity of the blessing, even if he did not hear the blessing. [Beis Yosef 124 in opinion of Rashi and Tosafus, which is the 2^nd opinion in Admur 124:11; See however Peri Chadash ibid and Mamar Mordechai 124:11] Other Poskim rule that by a Chazan with a Minyan, one fulfills his obligation if he answers Amen to a blessing, and he knows the identity of the blessing, even if he did not hear the entire blessing but only its end. [Raavad brought in Michtam and Rashbatz and Meiri Brachos 47a] Some Poskim rule that by Havdalah one fulfills his obligation even if he only heard the end of the blessing. [Rav Fisher in letters printed in Maor Hashabbos 4]

[5] See Michaber 183:6 and Admur 183:10 that if one talked in middle of Birchas Hamazon which he is hearing from another person, then if he talked in middle of the blessing he does not fulfill his obligation. However the M”B 183:26 limits this only to a case that one did not hear the parts of Birchas Hamazon that are obligatory to be said. Thus, seemingly the same would apply here to Havdala that if one did not miss any of the main Nusach he has still fulfilled his obligation. [See Piskeiy Teshuvos 271 footnote 105]

[6] 1^st opinion in Admur 124:11 and so he concludes to be stringent like this opinion; M”A 124:13; Bach 124; Admur 124:1; Michaber 124:8; Rabbeinu Yonah Brachos 35a; Rosh Brachos 7:17