If I start lessons in Illinois and I move to Colorado can I continue lessons without losing the hours that I have accumulated?
Welcome to the forums and thanks for posting! Yes, your flight hours will always count towards meeting the FAA minimums, but it isn’t just about that. You will likely need to brush up on your flying after a period of time off so there will be a need for some additional flight time.
If you are doing your training with ATP they are most likely going to want you to start and finish your training in one location. This is for your benefit as there is not really a lot of time for breaks in such an accelerated program.