As I have told the Rov, I zoom almost daily a good friend who is in hospital talk to him and often learn Torah with him. Is there a point to blow the Shofar of Elul to make him feel better?

Horav Shlomo Miller’s Shlit’a opinion is that it is correct if it makes him feel better and it is part of the most important mitzva of Bikur Cholim. The Rov added that you should make clear to him that this zooming method cannot be used on Rosh Hashana itself, even when offered by some Jewish services at that hospital. See question 3105 and 2325 regarding someone in a similar situation taking part of a family Pesach Seder on second day Yom Tov using a zoom monitor left on before Yom Tov.