Basically, you were teleported from the starter place (place A) to another place (we'll call it B) in the same universe with data. Afterwards, the player leaves place B. How would I save the data in place B, and call it in place A?
I'm pretty sure not automatically, but you can send the new data back to the menu when you are being teleported back. There's quite some documentation on teleport service, so you may want to take a look at that.
Happy Holidays! :D