If he's left eye dominant or, if I understand correctly, is forced to use his left eye as his dominant and shoot left handed, get a left hand bow. Period, full stop...
I'm left handed and when I was starting archery in my single digit years (in the 60's), I was given a RH bow by an uncle who knew absolutely nothing about archery. Back in those days, they just tried to make LH kids right handed.
So I shot cross handed (RH bow shot LH) for years, and it was nothing but frustration. When I finally learned bows were made LH and got one, it was like a miracle...