I have a friend of a friend who is sick.
If I directly talked to the sick person I would say:
I wish you would get well soon.
But I want the first friend to tell the second one. So something along the lines:
Could you wish him a ... for me?
If it was his birthday I could say:
Could you wish him a happy birthday for me?
So how do you ask someone, to tell his friend that you wish him to get well soon?