I'm not a lawyer, but I think you could purchase it, then gift it to him. This assuming he can legally own a firearm where he resides, and you don't make it a regular thing by buying firearms for all your "friends" on a regular basis.
But a one shot deal I think is permissible. He can send you a check because the ATF doesn't govern money, or amounts paid. Just the guns it can buy.
A "straw purchase" is defined as knowingly purchasing a firearm for someone who you know cannot legally own one. That is not the case here.