When you move house, you are still responsible for your Feed in Tariff for the remainder of its length. You can retain ownership of the tariff in theory, but this will involve relocating your setup to your new home. And this may prove problematic.
As a rule, ownership of the Feed in Tariff automatically transfers to the new owner of your home. While you may not be able to sell the tariff to them directly, it can certainly add to the resale value of your property, and offset your liability in this way. Talk to your supplier about how to transfer the tariff to your home’s new owner, as different suppliers have their own rules and guidelines.