It is very very unlikely that you can switch universities just before submission in this way -- you can sometimes take your PhD project, in its very early stages, from one university to another (even this is rare) but you can't make a last minute switch like that at any place I'm aware of. The only option is to drop out and start again, applying for separate funding and for a whole new project, but I'm sure you can see how self-defeating that would be. Even proposing this idea to anyone in authority at your university is a terrible idea, which has the potential to wreck your relationship with your supervisor, your reputation in your field and your references for future jobs. Just finish and shake the dust of the place off your feet.