How do you move existing houses to the Floating Island?

I can’t for the life of me figure out how to move the houses to the floating island. I’ve already gone into the inventory, and I’ve tried to see if there’s a way to store them in my bag or something—but there doesn’t seem to be an option. I’m playing on the Switch, if that makes a difference.

My goal is to relocate all the houses to the floating island. Pls help.