Normally, the control serial number is on silver tags on the back of the M39 pendant and also on the door of the control cabinet (if the control has a factory cabinet).
However, it is the CPU board inside (CPU7, CPU10, MPU11, etc.) that really identifies which control is which, since it is the CPU board that carries the software license.
The company that built gfacer2's control mixed components from multiple kits, so he has the hand pendant from one system, and the CPU7 from another. Therefore his control serial number is not the one shown on the back of the pendant.
If in doubt, e-mail Centroid with the "System ID" code displayed on the F1/Setup screen or the F7/Utility -> F8/Options screen. That code is based on the CPU board identifier, and can be used to look up your control serial number.