The 180 SST is a great bullet for the 06. Elk are tough and it was most likely dead on its feet with the first shot. I shoot 165 nosler ballistic tips @2820 out of my 308 and its one and done every time out to 450 yds. You don't need a premium bullet in slower cartridges IMO. SST and BT work...
Have him shoot a .22LR for practice and then let him shoot the deer with your rifle. He will never notice the kick. I have done this with all 3 of my sons. They shoot my 308 only when it's time to kill and they never develop a flinch. 22 is the greatest caliber for making a marksman...