Can I change which Mac the touch ID on my magic keyboard works with?

I initially installed my magic keyboard on a different Macbook which I am getting rid of, but now I would like to use the touch ID feature on a different Mac. It is Magic keyboard 2.0.6 with numeric pad and touch ID.

Is there a way to permanently switch? The keyboard works wirelessly with the new mac, just not the touch ID feature wether connected by cable of not.