[T-Mobile, Samsung Galaxy SIII] dakunclear:
Also note that your phone version is T999V so make sure you pick the right one for your phone

Information is provided by msoren8

Step 1. First, I suggest you to reset the ODIN binary counter by using TriangleAway app. At the time of this blog post, TriangleAway app does not support T-Mobile or Wind Galaxy S3 SGH-T999 but by the time you read this it might be supported so go ahead and download the TriangleAway app apk, install, and see if it works. (You can download it here on XDA, you will have to register for a username, it’s free.)

Step 2. Next, we are going to use ODIN to flash an official stock ROM for SGH-T999. This process won’t increase your binary counter so if you’ve used TriangleAway app to reset the counter, you should be all good to go. Also you can use Mobile ODIN too if you don’t have a Windows computer (but again, Mobile ODIN is not supported at the time of this writing but probably will be by the time you read this).

Hold down Volume Down, Center Home, and Power buttons together for about 10 seconds until your SGH-T999 resets.

Step 3. When your phone resets (screen will go blank), let go of the Power button but keep holding down Volume Down and Center Home buttons.

Step 4. Once you see warning screen, hit Volume Up key to enter ODIN Download mode.

Step 5. Connect a microUSB cable from your SGH-T999 to your computer.

Step 6. Download Odin and Galaxy S3 SGH-T999 stock ROM and unzip both files, you should find two folders like shown below.

Download ODIN

Download Galaxy S3 SGH-T999 Stock ROM

Step 7. Double-click on odin3 v1.85.exe to launch ODIN program. You should see a yellow highlighted box with a random number. If you don’t, you don’t have drivers installed. Simply download and install Samsung Kies. After installing Kies, don’t run Kies but simply unplug your phone and plug it back it, you should see yellow highlighted box now.

Step 8. DO NOT TOUCH ANYTHING but click on “PDA” and choose the file “T999UVALEM_T999TMBALEM_T999UVALEM_HOME.tar.md5″. Then hit “Start” to start the unrooting process.

Step 9. This process should take around 10-15 minutes. Don’t use any other programs on your computer during this process as it can interfere.

Step 10. When it’s done, your phone should reboot and you should find your T-Mobile Galaxy S3 SGH-T999 completely back to stock ICS ROM with all of your settings and apps in tact.

Step 11. If for some reason you are getting a lot of FCs (probably if coming from custom ROM), bootloops, or you just want to reset your phone completely to return for warranty you can do a factory reset. Otherwise you can stop at Step 10.

Hold down Volume Up, Center Home, and Power buttons together for about 10 seconds until your phone resets.

Step 12. When your phone resets (screen goes blank), let go of the Power button but keep holding down Volume Up and Center Home button together.

Step 13. Once in stock Android recovery, choose “wipe data/factory reset” and choose “yes”. Then reboot.

Step 14. Once rebooted your phone should be completely back to stock ROM and also just like the day you got the phone.

Remember, you still have to backup all of your personal photos, videos, and other files in your internal storage/microSD card and erase them if you are going to return your phone for warranty.