Sadly it doesn't carry over. If for some reason you'd like a refund I'd suggest doing the following (from personal experience):
https://support.google.com/googleplay#topic=3364260
On that page, drop down the "refunds and returns" -menu
in there "problems with in-app purchases"
In there, go to troubleshooting first, or if you already tried every trick/option in the book, go to "option 2"; contact support
That link will get you to a form you need to fill out, including your receipt number from the purchase you made.
State clearly what the problem is and as always, stay nice.
I hope this quick "guide" will reduce the time you'll try finding the right channels/links to go through...did for me and helped a lot of people with it
EDIT
Haven't read your post right.
Try and backup your savegame first:
-You'll need to get into your file system. I'm guessing Samsung has one pre-installed, but if not get a file browser (like ES File Explorer, it's free in the appstore and easy to use)
-Go to: /storage/sdcard/android/data/com.gamesas.falloutshelter/files/
-In that folder, there will be as many .sav files as vaults you created (for instance, if you made 2 vaults, you'll probably have vault1.sav and vault2.sav.
-These 3 files represent your vaults in ascending order, on the vault list (in game) from top to bottom
-Copy and paste where you want to back it up, or share to e.g. email.
Then, when your savegame(s) are safe, reinstall the game, that might do the trick.
HOWEVER if your savegame is 0kb (check by tapping and holding the file >properties) there is no use, and all data is gone.... sadly