I'm somewhat confused.
You pulled a working APU FADEC (or ECU - Electronic Control Unit) from the aircraft in question and installed it on another aircraft. Now you have issues.
Did you try putting the original ECU back in?
RPM is a fuel control issue. You stated you changed it. RPM's are fluctuating.
I'm I to assume it has a DC generator installed? If it's an AC generator, you can verify RPM's by watching the 400Hz output. If it's climbing and diving along with APU speed..... you still have a fuel control issue.