I can not in good conscious say it's a good idea to put (or leave) 15 amp receptacles on 20 amp lines. You can get receptacles that don't need adapters. They're very easy to find at a major store, such as Home Depot. In all likelyhood he won't ever draw more than 15 amps at all, let alone long enough to fry the receptacle, but as long as the possibility is there he should fix it. Like I said before, it only costs a couple bucks and can save your house. That seems like a worthy investment to me.
Also, we don't know exactly what will be on the line in the next few months when he makes his purchases because he doesn't know yet. We also don't know what will happen years down the road. Don't say just upgrade then, he may not remember. Just do it right now and there are no worries.