[Sprint Samsung Galaxy S III] Mr Stewart:
[SOLVED]

Here is what I did and it worked.

Bad phone = phone I want to flash/fix - - - - Good phone = phone I want take backup from

On Samsung Galaxy S3 you boot to TWRP by holding volume up + center home button then press and hold power button too untill you see some blue words at the top left of the screen, then release all three buttons.

Folder paths will be the same on your SD card but folder names will be different, see the note at the bottom about file names and folder paths.

What I did is run a backup on the bad phone in TWRP to the ext SD card in case anything went wrong. After it finished I turned the phone off and removed that SD card, then I turned the phone back on and ran a factory reset on the bad phone, when it finished and was at the first screen where you chose your language I turned the phone off. Then I inserted the SD card in my PC and found a folder with the file path TWRP>BACKUPS>551f9321>2016-03-03--18-28-10_2.01.11.0505 so I copied it to a folder on my PC and then deleted the last folder, the one that has a date for the name that had the backup files in it. Leaving the empty folders on the SD card TWRP>BACKUPS>551f9321

On the good phone I ran a backup in TWRP to the ext SD card, after it finished I turned off the phone removed the SD card and inserted the SD card in my PC, on the SD card I found folders with a file path like this TWRP>BACKUPS>9817290e>2013-12-31--18-55-59_2.02.11.0701, so I copied that to my PC(so I could return that phone back to its original state when this was all done) then deleted the dated folder off the SD card, leaving the empty folders TWRP>BACKUPS>9817290e on the SD card. With the SD card

OUT

of the phone I ran a factory reset on the good phone, when it finished and was at the first screen where you chose your language I turned the phone off. I booted in to TRWP and ran a backup to the ext SD card, when it finished I turned off the phone and removed the SD card and inserted it in to my PC, I copied the the dated folder TWRP>BACKUPS>9817290e>2013-12-31--18-55-59_2.02.11.0701 , to my PC and deleted it off the SD card, Then I took the original backup I made for this phone and returned it to the SD card so I could use it to restore the good phone in TWRP.

Back to the bad phone: I inserted the SD card in to my PC and copied the second backup I made from the GOOD (the backup I made AFTER the factory reset) phone to the folder file path TWRP>BACKUPS>551f9321>2013-12-31--18-55-59_2.02.11.0701 (this is the newer build number I am hoping fixes the Bluetooth issue on my phone) then I put the SD card back in to the bad phone and booted in to TWRP and ran a restore from the ext SD card, when it finished I was at the language selection screen!! I went thru the setup and let all my apps update from Google Play Store - entered my accounts in settings - and after all the updating I restarted my phone and tested Bluetooth.......................IT WORKS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! And I checked the Build number in Settings>More>About device>Build number shows 2.02.11.0701 = SUCCESS !!

Hardest parts:

1. Keeping track of which SD card is which(I used the phone cases I took off of each phone to hold the respective SD cards while not in use to keep them separated, I also noted the brand name of each just in case)

2. Keeping the backups organised - there will be a total of three backups, a backup of each phone and the backup made after the factory reset you use to flash the bad phone.

A word about file names and paths:

The first time I tried this I copied the entire folder path from the good phones backup to the bad phones backup, AND it didn't work. Problem is that the folder path has a unique number for each phone in it EXAMPLE -> TWRP(this folder name will be the same on all phones)>BACKUPS(this folder name will be the same on all phones)>9817290e(this folders name is UNIQUE for each phone)>2013-12-31--18-55-59_2.02.11.0701(this is the dated folder that contains the backup)