Hey. I think you’re an awesome friend and even if you don’t manage to get his short story published, I’m sure he’d appreciate your effort anyway.
To be honest, I have never gotten a short story published other than online and I’ve only written about 5 of them total, so I’m really not the best person to ask.
I’m sure it’s possible for the story to be published in a short story collection or magazine, but I’m slightly worried about the fact that it would be you theoretically getting it published for him; I’m not sure the collection/magazine editors would allow that? I feel like they would consider it off-limits unless your friend published it himself.
So I’m a bit unsure about that aspect, but what I CAN do is give you a list of magazines that you might investigate to see if by chance they will accept the story for publication (you can always explain the situation to them).
Winter Tangerine Review Magazine
All these magazines will have submission guidelines that you will want to read very closely to find out how to get the story submitted for possible publication; the guidelines might even explain whether or not it’s even possible for you to submit your friend’s story instead of him.
Good luck, and I hope you somehow manage to get this accomplished for him! Either way, I hope he has a great birthday.
Sorry I couldn’t be of more help!