The thing that is disturbing is the supervisor claiming to work the same hours at the two different jobs. There is at least the appearance of something untoward going on.
OP, you haven't replied to anyone's questions regarding what your role is in any of this. If you are in payroll and/or have a legimate basis to know the supervisor is actually doing this, then inform HR and/or the manager in charge and then leave it in their hand.

