My thots, for what it's worth
1. Stay away from any .22 centerfire for deer, even if legal.
2. .25 caliber bore is a good choice, .270 better. That said, due to his size and also depending on what type of hunting he'd do, a .243 might be an option -- but that's as light a caliber as I'll recommend.
3. You owe it to the animal you're hunting to make a clean shot and kill, and no head or neck shots. Get it in the boiler room, and the motor will stop.
Since he's been shooting, start practicing on the range, but from hunting stances, i.e., kneeling, leaning against a pole, etc. And, a few shots freehand just to show how difficult that is and what the consequences are!!
And, take him out and enjoy deer hunting with him!! Waidmannsheil, Dom.