Two Exact Same Chinese Phones, Different Baseband.


AC Question

I recently bought a Jiayu S3 from a retailer in China. I received the item and when I turned it on it didnt have Google play services or any Google apps on it.
As a result I had a phone that did not link up with my Google account which bothered me, so much so that I tried to flash it to a rom onto it.
Problem is I flashed the bootloader and then my phone was bricked. I sent it away to be fixed by the same company I had bought it off and they told me that they would give me a full refund once they had received the item back. I knew that by the time I sent the phone back to China so they could look at it and then give me a refund it would take a full 3 weeks. I just went ahead bought the same phone again which they told me definitely had Google loaded onto it.

That was fine, I got the new phone a week or two later and sure enough it had all the Google features I needed. I was waiting on the refund to come in one day when I got an email telling me that the phone they looked at was fixed and it was in the post, on the way back to me!

The problem now is I have two of the exact same phones, one working just fine and the other being in the exact same position I was in at the start.

What I want to know is, is there a way of backing up the working phone and then transferring that data over to the phone which is no good to me?
I'm afraid of flashing the phone again as I made a total mess of it the first time.

Any help would be graciously appreciated!