Thank you very much for this enlightening post :) Yes, my immobilister ist "disabled" by a unit which probably works as you described. I will try to use the 101040. If it works, that will be great as no hassle with the immobilister any more.
My garage suspected the ECU as the stepper motor does work correctly but is not correctly controlled by the ECU. Also the relais of the fuel pump has been tested which as well indicates (according to my garage) that the ECU is faulty
Additionally they discovered that water has entered the unit. So all is pointing at the ECU.
Thank you all for your responses. I will surely post back as soon as I have the result :)