if he can train himself to close his left eye whilst keeping the right open, he can train himself to shoot right handed. my wife has the same issue, almost put her off shooting. I've since started training her to shoot left handed, and apart from the awkwardness, she's getting on with it well and couldn't believe how amazing it was to be able to "see what I'm shooting at" ! LOL..
are you sure your son is right handed? I understand a lot of left eye dominant people are inherently left handed, but were just wrongly taught to write right handed in school, etc...whereas, once they 'try' left handed, they become much more proficient!
so yes, either, serious eye training needed, or learn to shoot left handed!