Am I allowed to answer a bracha over the phone or a recorded bracha? Where can I find this halacha?
The common custom (certainly for Ashkenazim) is not to answer Amen for blessings a person hears over the phone.
Rav Shlomo Zalman (Minchas Shlomo 1:9) writes that the case is apparently similar to the shul in Alexandria (Sukkah 51b), where people answered amen after seeing raised flags, but could not actually be yotzei with the chazzan’s berachah (see Tosafos, Sukkah 52a). According to this comparison, one would answer amen to the berachah, and this is the ruling given by Rav Ovadyah Yosef, and by some other poskim.
However, Rav Shlomo Zalman rules that it is possible that the case of Alexandria is different, because one is present in the same room, and therefore rules that one should not say amen to a berachah heard on the phone, where one person can be on the other side of the world, and the two are not “joined together” by any geographical factor.
The common custom is to follow this ruling, and not to answer amen for berachos over the phone. However, it is correct to nod one’s head as an alternative to answering amen, as we find in the Gemara in Berachos (7a).