When I was younger, I had already learned all about safety, and was proficient with most guns. Before my father would let me hunt with a larger gun, he would take me out, set out a paper plate at a certain range, and tell me to put 5 rounds straight through it. If I could do it, he would take me. It worked that way from spruce grouse with a .22, to moose with a .30-06.
Test him, on safety, on lawful game, on shooting, on everything. If he does it well, then he is ready. If he is lacking, then he needs to learn and practice more.