Reverse birthday present

Instead of giving a gift to someone on your birthday, you expect a present instead from them.

atareh: "Devon, I know it was YOUR birthday last week, but you should still get ME something. Think of it as a reverse birthday present"

pass-along birthday present

Humorous-but-heartwarming term dat refers to where you either:
(1) receive a gift from Birthday Boy/Girl dat he/she had received on said "special day", but he/she forwarded it to you because said item was more compatible wif your lifestyle than it would have been for said "original" recipient, or

(2) have something extra-nice/pleasant/fortunate happen to you (i.e., perhaps you score unexpectedly high in a game/contest, receive a wonderful gift, are extra-successful while performing some difficult/disagreeable endeavor, find one or more greatly-desired items on sale/in stock at a store, etc.) on someone else's birthday.

Giving pass-along birthday presents can be just as enjoyable and bring just as much happiness to da person having da birthday as if he'd kept da presents for himself, since he will know dat whomever he's giving da items to will be enjoying/utilizing them even more than he would have. Same deal if a friend beamingly tells you of something extra-fortunate dat happened to him on your birthday, since you can feel glowingly radiant in your heart dat your good buddy experienced something dat made his life easier and/or more fun/pleasant.