This is a 2 parter question.

1. How do I move one shop to another?
2. How do I move my vault to a shop?

For vault to shop: Go to your vault and check all the items you want to move, scroll to the bottom of the page and find "Destination:" click the dropdown list and select the shop you want.

I don't know if you can move one shop to another.

If you still have a Legacy shop, it's possible to move items from that shop to a new shop using the dropdown at the bottom of the Edit Shop page, but otherwise it's not possible without moving all of the items to either your inventory or your vault first.