May one be yotzai listening to havdala over the telephone?
Most Poskim say that if another option exists, a telephone should not be used to fulfill the mitzvah of Havdalah. Rather a woman who is home alone and has no one to make Havdalah for her, should recite it herself (Mishnah Berurah 296:35 - Aruch HaShulchan 296:5) rather than listen to it over the telephone. Even if the lady can not drink wine, grape juice, or beer, it is better for her to recite Havdalah over coffee (Shmiras Shabbos K'hilchasah 60 note 18) tea or milk alone (Aruch ha-Shulchan 272:14; Igros Moshe O.C. 2:75). According to some poskim (Tzitz Eliezer 8:16; Shemiras Shabbos K'hilchasah 60:5), it is preferable to drink grapefruit, orange or apple juice rather than to listen to Havdalah recited over the phone.
If you are in a situation where you cannot recite Havdalah (in a hospital), and there is no one who can come until Tuesday evening (Orach Chaim 291.6) to make Havdalah for him, he may have to rely on the poskim who permit listening over the telephone(Igros Moshe O.C. 4:91-4; Tzitz Eliezer 8:11). But in a situation where someone could come and recite Havdalah for him before Tuesday evening, the correct procedure is to wait until then for Havdalah to be recited.
It should be no different than any other halachah where you have to hear something. You can't be yotzei by hearing shofar, or megillah, or the like over the phone (will have to find the source for this), because you're not hearing the original sound but a re-creation of it from electrical signals; the same presumably applies to havdalah.
The Lubavitcher Rebbe wrote (with regards to Megilla, Shofar, and Gittin) that in contrast to an acoustic hearing aide whose amplified sound is connected to the original sound, a sound produced through a microphone (or telephone) has no halachic connection to the original sound.
A microphone (or telephone) works by a voice changing the electric current which produces a sound at the other end. Halachicaly, this would be just like computer-generated words, which one could not be yotzei with. The Rebbe pointed out that many of the poskim who ruled otherwise were misinformed as to the inherent nature of electricity.
One may not answer Amen to such blessings. Rebbe in Shulchan Menachem 3/319; Daas Torah 689 based on Halachos Ketanos; Mahraiy Engel Brachos 25; Minchas Shlomo 1/9; Eretz Tzvi 1/23; Minchas Yitzchak 1/37 and 3/38; Yechaveh Daas 2/68; 3/54; Mishneh Halachos 4/85; Kinyan Torah 1/75; Igros Moshe 2/108; 4/126 [not to do so initially]; Sheivet Halevi 5/84; Beir Moshe 3/166-168; Piskeiy Teshuvos 689/3
Other Poskim: The following Poskim are lenient are permit hearing the Megillah through a microphone and the like: Minchas Elazar 2/72; Mikraei Kodesh 11; Tzitz Eliezer 8/11; See Igros Moshe ibid that his leaning opinion is to permit being Yotzei and that so should be done in a case of need, that one is unable to hear Havdala otherwise.