Is it permitted to send regards to a person’s wife through her husband in a phone conversation?
It is permitted to ask her how she is, and to inquire about her, but a man should not send regards to a married woman, even via her husband in a phone conversation.
One can perhaps “send regards to the family,” provided there are other family members that regards can be sent to, other than the wife.
Sources: Shulchan Aruch, Even Ha’ezer 21:6; Chelkas Mechokek and Beis Shmuel; Magid Mishnah, Issurei Biah 21:5, makes the distinction between inquiring as to her wellbeing, and sending regards; see also Taz, who makes a similar distinction. The poskim discuss sending regards in a letter, but the same would seem to apply to a phone conversation.
There is room to investigate whether the ‘regards’ of today are the same as the shelominthat poskim refer to (for instance, Taz writes that sending Shalom is prohibited because it demonstrates one’s affection for her, a description that might not apply to ordinary regards, which can be a matter of courtesy). Yet, I have not seen this distinction made by halachic authorities.