I’ve read that Nicholas Hooper got inspired by Williams’ score but I can’t remember him reusing any of the old themes other than Hedwig’s theme and the quidditch music from PoA. Hooper’s scores are my favourite ones, so I’m glad that you put some of it into the other movies.
Then he probably was more inspired of the actual tone and sound of his score, rather than the musical cues. I really loved Hooper’s score for HBP, but I found the score for OotP very, very boring and unimaginative, with few exceptions being Sirius’ new theme (but why the f*ck would you even make a new theme when you have A Window to the Past!).