Okay, here we go.

So I had a vault I had invested all of my time into and was very fond of. Then, in July, I broke my Moto X phone (shattered the screen - the screen is completely unusable and doesn't display any images).

I was very worried about losing my massive vault, so as soon as I broke my phone I plugged it into my computer and copied all the files that looked related to Fallout Shelter (it seems there are just two folders that do that: Internal Storage>Android>data>com.bethsoft.falloutshelter and Internal Storage>Android>obb>com.bethsoft.falloutshelter).

So I have all the files related to the game on my computer. When I first received my new phone, I installed the game again, although it is at a newer version now. I tried replacing both files I spoke about above in the new phone with the ones from the old phone, but after doing that the game won't open (it goes black and then closes).

So how do I recover my vault from my old phone to my new phone if I have all the files?