Integratred training transfer needs CAA approval. Transfer of hours towards modular groundschool if that is started but not complete would likewise need CAA approval. I would expect it to be automatic in both cases if the school had gone under, as it was for those I taught at SFT's groundschool who then finished off some with the help of our instructors and took the rest elsewhere. The CAA were as flexible as they could be - I even had delegated authority to finish one guy off in my subject "training as required".
Course notes must go with the student for modular flying courses, but we have had people complete CPL courses here who started elsewhere.