Originally Posted by
Segev
I am generally of the opinion that honesty and openness are for the best, but if you are too uncomfortable with it...
A possibly solution would be for you to roll a die in secret for him. Report the results as if he'd gotten what he says he did, but don't modify hit points or "fudge" the monster's ability to evade less-invisible consequences (such as being grappled).
As far as avoiding letting him steal the spotlight, that's a matter of plot focus more than general combat success. Do your best to incorporate the other players' characters appropriately. Let them have their heroic moments by simply not letting the cheating overshadow them. This shouldn't be too hard since you're handling the cheating by ignoring results that your dice tell you were failures. Even if you don't report that he missed, the fact he didn't do damage (even if you let him report damage rolled) means the monster isn't going down, so the other players have their shot.