Get the files of FGO in your phone
Main Storage/Android/data/com.aniplex.fategrandorder
get the cache and files folder. It should be around 13gb right now.
Compress it using winrar or 7archiver and save it somewhere on your PC or phone, save that backup.
When you want to use a different device, install FGO on that device, and then once you are on Main Screen, close the app. Then, put the files of your FGO backup in the same path I mentioned above (Main Storage/Android/data/com.aniplex.fategrandorder). You also don't need to use your transfer code, although you will need to configure your ingame settings again (like the battle speed, etc).
And any files you need to update will be done in the options in-game. Don't worry, it will read all the files you have and you don't have to download 13gb+ of content again.