Hi,
I actually thought that the engine control unit would read the mileage from the instrument cluster when error entries are made, but okay.

On its own, I would say there is no sufficient indication of mileage tampering.
Before doing anything with the injector, of course, check the wiring and connectors.
If everything seems okay, disconnect the plugs from the injector and the one next to it. Then, use a multimeter to measure the resistance between the injector terminals and from the terminals to ground (for the injector). You might notice something when comparing the readings. If possible, a capacity measurement comparing both injectors would also be beneficial.
Background story:
Okay, I'm ready. Please provide the German text you want me to translate.
Best regards, Rainer.