You will either need to use a program to change your new vault to get however many box's and mr.handy's and such and you can find those easy with a google search or file a complaint with google support to get a refund as they will be how you get it and report the issue again saying bethesda refuses to refund you as others have done.
Sadly the game does not sync with other devices or back up your save and it is a issue for a mobile game that they seem to have overlooked for whatever reason although it does mean you can play the game offline and changing to either of these could upset people that play the game because of that.
In either case make sure you back up your saved vaults daily in the future if you continue to play.