The Biur Halacha in Siman 299 brings an interesting opinion from the Magen Avraham. If someone was fasting (and had taken on to fast for a few days) and wasn't able to make havdallah Motzei Shabbos and when it came "lyl gimmel" it was also Rosh HaShanah the Magen Avraham says that the person should make havdallah on one cos and kiddush on another cos (and not to make them on one cos.) The Biur Halacha has a very difficult time with this and says how can someone make the bracha of havdallah and end off "bein kodesh l'chol" when it's right now Yom Tov? To say bein kodesh l'kodesh he says one also couldn't say. The biur halacha leaves this din b'tzrich iyun gadol. Were there any other poskim that discussed this Magen Avraham and perhaps offer an explanation or discuss (and possibly answer) the questions of the Biur Halacha?
Rav Dovid Feinstein was asked this question and he answers in the sefer L'Torah V'Horaah pg.28
The person asked what should he say since the Biur Halacha ends with a tzarich iyun.
Rav Dovid answered ,it seems to be reliant on a machlokes Rishonim.Is it a tashlumim or do we say a chyiuv is on him still.He brings the Rosh from perek mi shameisu siman 2 that one who is a onein on motzai shabbas does he say havdsllah or not.The Rosh brings the Ri who says that it is a tashlumim and if he was patur then he doesn't say it,the Rosh is maskim to this.However,he brings the Ram who says he is obligated in havdallah and the Maadnei Yom Tov os 3 holds the time is extended up until the third day and the Mechaber paskens in YD 341:2 that he should make havdallah.In the Mishna Brurah siman 71:1 its mashmah a little that he paskens not to say havdallah even though from the מלבושי שרד its mashmah lav davkah.
Rav Dovid then writes ,it seems to me that if it is a tashlumim then its shayich to say Ben Kodesh lchol but if the chiyuv is straight then it should be Ben Kodesh lkodesh and the issur of eating is still on him .The MA writes in 299:17 that it is assur to eat all times until one makes havdallah.It seems to me that is not like the MA ,but what can we do,since the MA paskened this way we have to go like him.
wrote from my phone,please fix mistakes,and read inside.