transferring purchased wall/ floorFollow

Is it possible to retain the options one paid for in a 1 bedroom type 1 and bring them into a 1 bedroom type 2 or larger space?

The question is whether you keep the "polished obsidian" wall option you just spent 20g for when you move into a new place. Is this still something that can be reset for 20s in the new place or do you have to drop another 20g if you want obsidian walls in the new place?

Yow! Thanks.