Thanks Keith for your response,
For clarity and perhaps to help others, if there are many..
I was in contact with the Federal Ministry Climate Action, Environment,
Energy, Mobility, Innovation and Technology and they said:
“After consulting the competent department, we can inform you, that due to the information
you gave us, we cannot explain, why you cannot exchange you driving license. Therefore, we
recommend to contact another Führerscheinbehörde and ask, if they may change your
license.”
After visiting a different BH I was able to change my driving licence over to the Austrian one without any fuss.