Either teach him to shoot left handed or to close the left eye when the cheek hits the stock.
I was right handed and left eye dominant.
As I began to age, I acquired central vision, that would switch to left dominance with fatigue.
Shotgun sports (which demand having both eyes open during sighting) were problematic.
Luckily I shoot Churchill (English) style, that is tracking the target with my eyes, buttstock at my side, pivot body, mounting the gun and firing as the buttstock hits the shoulder.
At 28 years old, after the dots on the glasses, trying to shoot left handed, leaving one contact lens out, etc. I finally hired a coach for three hours.
He told me to keep both eyes open until the wood hit my cheek, then slam the left eye shut.
I actually began to run 25+ at skeet, was amongst the last men standing and splitting the pot at cutthroat trap, and was mailed a tiny bit of NSCA $$$.
Rifle shooting, which I was okay at but never pursued competitively, was always a right-eyed affair.
If the boy can see fairly well out of the right eye, let him use it.
If there is a compelling reason, give him a left handed rifle.