Whenever you move from a district that is no longer considered your "home school" so the child is no longer supposed to go there. If you live in a district and move mid year for example, you will have to go to the district offoce of your home district or school and request whats called a release from their district. Once that it approved (can generally be done that day), then you will take the stamped form to whatever school you are wanting your child to attend and apply for the transfer, attaching the release with it. Transfer approvals at that time will take up to 4 to 6 weeks to be approved.
Living in a certain district for any certain amount of time has no bearing on whether your child can go to any school. your home school is the closest to where you live. You can go to that school the day you move. you will need no transfers. Your childs old school can also have all folders and paperwork transferred for you also. Your best bet is to give the current school notice of your childs last day and make an appointment for paperwork enrollment at the new school.. High schools are generally done by apt. By the sound of your situation, you no longer live in the district so you will need the transfer which like I said, is done thru the district. Unfortunately the school itself has no control over that.
Hope I answered your question. Good luck to you :)