You can actually manage this move pretty simply! Through your panel, you'll need to create a username on the intended server, and then you can add new domains or modify existing domains to use that username. Our web panel will then offer to migrate the data for you. This link will help (it goes the same way to move a domain back to shared):
Of course, if you have any trouble/questions, or need help with any of this, please don't hesitate to contact our support team via the panel. As ottodv can attest, we'll be happy to help!