Is the game crashing while in the loading screen or when you already actually see your vault?
I'm curious about this, because there's a lot of people out there with crashes that are either during loading (0kb savegame) or after about 45 seconds (normal size (for me 200-400kb) savegame)
I know this isn't going to help you now, but do you know already how to make backups?
-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.