First that is what he's supposed to do. There is a lot written about how missionaries who pay for their own missions perform at a higher level. And the handbook of instructions says if possible the missionary should pay for their mission.
That said, I don't think there is anything wrong with you actually transferring the money to the church and taking the tax deduction. Just let your son know that is what you're doing. Give your son a gift equal to the money he pays. Put it in a Roth IRA. Whatever you want. But let him know he paid for his own mission.