Furnace heat duct for basement
You should be able to find a piece of duct at the big box store to extend the boot to the wall. You'll need to trim it with a good set of tin snips. When you trim it leave some tabs so the register screws have something to bite into instead of just drywall. Get a larger register that better matches up to the duct. If you can't get the duct to line up with the register then see if you can rotate the boot and cut the duct at an angle. If you don't do a great job then get some foil duct tape to cover any gaps.