It should be listed in his DD-214 or in his Service Record. All awards are listed in the Awards Section of the DD-214 and each individual award gets a page entry in the Service Record. He had to have been qualled as some sort of shooter, at some point, to be allowed to continue in the Army past the rank of E-1. If you can't get a basic Rifleman Badge, you get booted for failing to adhere to the regs.

Edit: the only group of service members I know of that don't have to qualify are the Chaplain's Corps. The rest, even a Corpsman/Medic, have to have at least a Basic Rifle qual to get past the "boot phase" of training. I know some people in every branch that had a hard time with shooting and were held back from advancing out of Boot Camp/Basic Training until they qualled, and I know of a few who ended up Admin Separated at the 181 day mark of their enlistment for failing.