I am going to go against the majority on this one and suggest for him to close his left eye. This will, by way of elimination, make his right eye dominate. In my expierience, when shooting for pinpoint accuracy with sights or a scope, most people close their off hand eye anyway. What I do when wingshooting with both eyes open is I slightly tilt the bill of my cap down and left. It dosen't obstruct my vision, but is in the way just enough that my right eye really takes over to look right down the barrel.
Also, this is a right handed world and sometimes it can be a pain to get left handed weapons or shooting accessories. At any rate see what works best and is the most comfortable for him.