It depends.
Look at the detailed description (p121 of the revised edition), and it should be clear. The hunter keeps those things that they should keep, and discards those that are left behind by this change.
Sometimes a hunter keeps all their moves, sometimes they might keep none. There's no overriding rule here, because it always depends specifically on the experience of the current character and the change they go through.
For the advanced moves, ask yourself if they are starting again from the beginning or if the hunter can still use the experience they have already gained.