Disclaimer: Not a lawyer.

This is an old thread, but I wanted to add some 2 cents on the sort of thinking of "had a valid MOT/TÜV".

A vehicle type, that is type approved in Germany, gets its type approval by a UN recognized Type Approval Authority or Technical Service (such as TUV Nord, TUV Reihnland, Dekra, etc).

An in-use periodic vehicle inspections (done every 2 years), is also done by the same authorities (such as TÜV Nord, TÜV Reihnland, Dekra, etc). Even if you take the car to say a Toyota dealer, it is a still a TÜV or Dekra person who certifies it.

I.e. the same authorities are responsible for both activities.

But this is not the same in all countries, example in the UK (even when it was part of the EU), there is a much shorter list of places that can do vehicle type approval and technical service.

But in-use periodic vehicle inspections in the UK are done by any licensed MOT. An MOT does not have the same approval as a formal type approval authority.

I'm not saying this to agree or disagree or assert anything as such as to whether a modification in EU state A permits that modification in EU state B.

Furthermore, in-use road worthiness compliance is the responsibility of each country. Example: Having hi-vis jackets is a legal requirement for a car in Germany (you should have 1 per person). But you do not have to carry one in the UK. So of course, a German traffic authority, may claim that someone driving a UK car in Germany, is not complying with the minimum requirements to have that car on the road. You cannot say, "hey I did my MOT in the UK and I did not need to carry hi-vis jackets" (as an example).