Before you purchase a Left Hand rifle, it might be worthwhile to check his eye dominance. If he is right eye dominant, he will be much further ahead to learn and build muscle memory of shooting from the right side (dominant eye) with the current Rem Model 7 that you have already purchased.
IF he is Left Hand dominant and Left Eye dominant, there are used Left Hand Rem 700's in .243, .260, 7mm-08, and 308, if you look for them. Also, Left Hand Tikka T3/T3X's for probably less money than the Remington 700's at the moment...
Eye dominance is the most critical part of this thread. That should always be checked, regardless of which hand he favors. He's more than likely left eye dominant, but its always best to check to be sure. I've been seeing more left hand Tikka rifles on the used rifle rack. That's what I'd buy, if it were me. Good luck with it and good on you for being a thoughtful uncle.. Kids need that..