Nice truck.
Yes, 31x10.5's are the largest he can run effectively without rubbing. Larger tires will fit, but will hit either the inside of the fender or the flare when turning and flexing, moreso if he has swaybar disconnects.
When he puts them on, he'll have to adjust the steering stops as the tires will rub at full lock. This is easy to do and you don't loose hardly any steering radius. Just take and back the stock bolts out and shim behind it with some washers, or do like I did and get a new bolt and nut for $0.25 and adjust them yourself. I prefer the new bolt and nut because it allows you to get exactly the right radius for the rim size, mine don't touch, but there is less than 1/8" inch before it could. The original nut is tack welded to the bolt, so you can't adjust them.
I have been running 31x10.5's for the last 75K on the wife's '97 TJ, and a bunch of different brands, they'll work fine and won't rub.
If he hasn't already done so, have him get some swaybar disconnects if he's gonna wheel it, it's the single best thing he could do to improve its driveability off-road. He will get very minor rubbing on the top of the coil tower at full flex with the 31's, but it's nothing. Front swaybars only, the rear saybars offer very little additional flex (like 5 points on a 23 degree ramp, I measured mine).
JEEPN
Winter Harbor, Maine
'81 CJ-8 Scrambled, It's a Jeep, Chevy, IHC kinda thing!
'88.5 Zuki, 5" Calmini, Locked, Swamped, Rolled, and just generally broken in right!