Maintenance Controller described an incident where he had a mechanic rob the #3 AUX NAV Receiver from one aircraft and install it on another to put the aircraft back in service. While the Controller was filling out parts tags; he checked the compatibility computer and found out the NAV Receivers were not interchangeable. The aircraft flew one leg before Maintenance was able to remove/replace the #2 NAV Receiver with the correct box.

Narrative

Aircraft 'X' arrived into ZZZ with #2 VOR System inoperative; with no AUX NAV Receiver; aircraft was grounded. Found that another B737; Aircraft 'Y' was also there with #1 engine start valve circuit breaker popping. I made the decision to have Contract Maintenance in ZZZ rob the #3 AUX NAV Receiver from Aircraft 'Y' and install it on Aircraft 'X'; at the #2 VOR side so we could get one aircraft flying again.Installed NAV Rec on Aircraft 'X' and Contract Maintenance performed operations check of system with no faults noted; finished up logbook and downgraded HUD (Heads-up Display) system; released Aircraft 'X' for service. Contract Maintenance then went over to install bad NAV Receiver into #3 AUX position on aircraft 'Y' and MEL'd AUX Nav Receiver.While filling out robbed parts tags; checked the Maintenance Parts compatibility computer and found out NAV Receivers were not interchangeable. Grounded Aircraft 'X' right then in ZZZ and sent correct NAV Rec and mechanics to ZZZ. Aircraft 'X' had already pushed off the gate and departed before I could stop it. Aircraft 'X' flew one leg to ZZZ1 where aircraft Maintenance R/R'd (Removed/Replaced) #2 NAV Receiver with correct box and upgraded aircraft.