I think a warning is in order if it hasn't been given already. That warning should include the stipulation that if he clocks one more bogus minute, he's gone.
I am a bit of softie when it comes to this stuff though, and have ended up keeping employees around for much longer than I should have in the past. If I would have canned those guys when most here would have, it would have probably saved me a lot of time and money. But almost all my employees are friends or friends of friends, so it makes it a lot tougher to be a boss.