It has happened before:

At the beginning of the war when the Germans were rambling all over the place lots of the national coppers stayed put.

Liberation of Java at the end of the Second World War - the Japanese although defeated remained as the civil administration, police, army the whole shebang under the command of Allied senior officers.

Same thing in East Germany - joke was Hitler's ex police just changed caps. Head of criminal police in East Berlin was quite high up in the SS Krimpo (?) All done on the premise that ordinary/normal crime still goes on and a good copper is always a good copper and they know the turf

If the guys (US) who came in and didn't know about the background, they might of viewed it rather cynically as a stitch up and removed them as the people in power on arrival thinking THEY were the former ones in charge - bit of a stretch of the imagination that one, but no way of knowing what the riding instructions were at that time.