I say try the one handed backhand.
I myself used the 2 handed backhand for 7 years, never quite getting it. I switch to a 1 handed about 1 year ago, and am hitting it clean and crisp, way better that I ever did with 2. Don't be afraid to switch. Even the great Pete Sampras had a 2 hand backhand until he switched to a 1 hander, and he's one of the best ever.
When perhaps for a long time you try out a particular shot and you feel you aren't getting anywhere, then yeah, of course it makes sense to try to change up your game. However, I don't think suggesting him to try one-handed is a great idea at all because of his lack of experience.. I myself used to be a two-hander, and it was my best shot. However, my private coach at that time had me start practicing one-handed backhands to see how that felt, and after several months, I felt much more natural with the one-hander. If you notice, many of the top players in juniors and pros, actually know how to hit both a two-hander and one-hander very well, and that is honestly the only true way to decide which you are. In today's modern game, using a two-hander is a much safer bet, considering the fact that you can deal with higher balls much more easily. Either way, the only way to decide is you can practice both shots and then after a while decide what feels better for you and your game. To just drop one and go for the other makes no sense, as I've seen plenty of juniors over the years go from a much more normal looking two-handed backhand, to something absolutely fucking atrocious they call their "one-hander" thinking that they get Federeresque powers.
Just to do a quick analysis to help out a little more comparing the two shots-
1. I still think that in terms of pace and spin, a great one-hander can produce more than a two-hander
2. May be more natural as you may play other backhand shots one-handed like the slice or volley
3. The shot is heavily based on timing considering they have much longer backswings than two-handers
4. Much better reach
1. You can MUSCLE the ball - this is the biggest difference and the reason why it is the dominant way of hitting a backahnd. While you can certainly "block" shots with a one-hander, a two-hander can do much more when placed in a defensive position as they don't require a lot of torque or a large backswing in order to generate spin, pace and get the right placement.
2. You can flatten shots quite easily. With a one-hander, in general you are naturally going to produce topspin even when going for winners because the stroke is typically start low, end high. With a two-hander, it is much like a forehand where you can start high and flatten out a shot.
3. A two-hander will struggle a little bit with their reach especially when returning serve - it'll cause them to either play the shot poorly, or take their off-hand off the racket which may also create a poor shot as well.