I have transferred now a bunch of buildings to the city. I have come to the following conclusion: I will NOT give the owners building rights once the buildings are in the city. It is just too much work to do and manage that.
So if you want to have your building in the city, I will copy it there unless you want me to remove it from your lot. Those people whose building was already moved by me, can get a copy of the building back on their lot. Contact me here and tell me where you want it. I will put it back.
If your building is in the city and you want to upgrade it or make considerable changes, please change the building on your lot and I will then overwrite the updated building in the city with the new one.