You can check the output from the Stator easily. With everything connected.
Switch you meter to AC voltage, ensure the leads are in the correct position for measuring AC. (Some may need changing others do not)
Push the meter leads in to any 2 of the 3 white wires at the rear of the connector coming from the Stator.
Start the bike leave it tick over voltage should over 16 volts AC. Rev the engine and the voltage will rise accordingly (could rise to 90 or 110 volts AC.
Be careful/cautious doing this as it can give you an electric shock
Engine off, remove one lead and put it in to the third wire. Start the engine and check the voltage again. If it rises according when revved the Stator is good.
The most common charging issue on the Fazer 600 or 1000 is the connectors burning out.
The fuel injected FZ1 model is a totally different ballgame the generator explodes in those much easier to find the issue