Here's how to root Samsung Galaxy S3 SGH-I747(AT&T) which is already updated and now runs with Android 4.1.1 Jelly Bean Software build I747UCDLK3. This root method is still the same process we used from previous Ice Cream Sandwich. The best part of this rooting process is that it will not trip the binary flash counter of your device. This uses the original stock ROM I747UCDLK3 which already injected with root system image. This root procedure was developed by MrRobinson an Elite Recognized developer from XDA-developer. This already proven safe root method beforehand and still the best root method for any future updates.
How to Install ROOT I747UCDLK3Grab the root injected I747UCDLK3 stock firmware:
Current I747UCDLK3 (JB 4.1.1) - NEW JellyBean
Mirror 1: Download root66_ATT_I747UCDLK3.7z
Mirror 2: Download root66_ATT_I747UCDLK3.7z
Grab Odin and USB Driver
Odin flasher - Odin3_v3.07
USB Driver - Samsung I747 USB Driver
Download and Extract the stock_root69.tar from the .7z file from the link above
Use PC with Windows OS (Odin will not work on Mac and Linux OSX)
Make sure to fully recharge your battery
Use the original supplied USB cable for your Galaxy S3
1. Run Odin on your PC desktop
2. Boot the Galaxy S3 into download mode screen for Odin.
Turn it off, once completely shut down hold down the 'HOME' + 'VOLUME DOWN' buttons and press the 'POWER' button for about 2 seconds until a WARNING! Screen appears. Press the 'VOLUME UP' button to continue or enter Download Mode.
3. Connect the phone to PC via USB. Then make sure you can see as phone "Added" in Odin log box or a highlighted COM:ID once the device is detected,
4. In Odin window, DO Not tick 'RE-Partition' only Tick 'Auto Reboot' and 'F. Reset Time' and nothing else.
5. Click the PDA button ten load the stock rom with injected root system image root66.ATT_I747UCDLK3.tar.md5.
7. Wait until the flashing finishes and the phone completely reboots.
How to UnRoot I747UCDLK3If you need to unroot, and restore back to original firmware. All you need to have is the original, unmodified and unrooted I747UCDLK3 stock ROM or any latest official firmware from Samsung. The installation process is still the same from above. But this time you need to load the original, unmodified and unrooted Jelly bean stock ROM on odin's PDA button. Just download the original firmware below, it is very useful to your device, in-case you need to unroot, restore your Galaxy S3 to original factory settings.
Here's the original stock ROM: (this is tested and safe files, pulled from Samsung Kies server)
See more details posted by mrRobinson here: http://forum.xda-developers.com/showthread.php?t=1739426