I've had a few dogs, not many, that I've fostered that were depressed for a while.

They do did get over it. Plus, I am very affectionate with my dogs and give them all lots of hugs, kisses and attention. They sometimes act like "okay, already." If I go by a dog, I touch her/him. I actually love the older dogs. Nearly every senior I've fostered has been easy. Hopefully if he knows you and you are affectionate with him, his transition will be easier. Dogs know how you feel about them, so love him and he will love you.
I don't know what agreement you have about vet expenses, but I can tell you, senior care is much more expensive. He should have routine bloodwork and a check up twice yearly. How are his teeth? If he hasn't had a dental lately, that might be something you want your friend to have done BEFORE she leaves. I'd also make sure your friend leaves you the money up front for emergency vet costs, too, unless you've agreed to take care of the expenses.
You are really sweet and a good friend to take her dog in. I predict it will be a rewarding experience for you and that you will come to love the dog as much as your friend does, if not more.