So, for unique district civs conquest becomes a pain
But why should it be different? Why should buildings/districts change to uniques when you conquer them? It would look weird. And it would be fun to conquer UDs that you cannot build yourself. Gives the whole conquering thing a new edge. Let Germany build their cities, fill it with districts and then take it over. Or do you think the extra free district should disappear if you conquer the German city when it doesn't have enough pop to actually support it anymore?
And when? When you conquer the city or when you decide to keep it after war?