This tutorial is based for App Fallout Shelter on the App player
In Fallout Shelter there is no way to sync your game account with other devices such as tab/phones or PC. However you can backup and transfer your app progress to another device.
Once your vault is created you can retrieve it by following the steps mentioned below:
1. The game on your Android device/PC is at the following location
Here 'x' is the value of your vault.
a) Install Es File Explorer on the app player using the steps in the URL below
b) Navigate to storage>sdcard>android>data>com.bethsoft.falloutshelter>files>vaultX.sav
c) Now copy the vaultX.sav file as shown in the images below.
2. You can access the data on your PC using the steps in the URL below
You can also refer to the articles below.