Samsung And T-Mobile have released the next update UVUENC2 for SGH-T999.
EDIT - @mrRobinson has a Root66 version of UVUENC2. That version is KNOX Free. So my recommendation is to visit his thread and using that firmware instead.
WARNING - The following steps are only for those who had accepted the previous 4.3 Update UVUEMJC or flashed it from Root66 thread.
Essentially with the newer updates to the Odin, version 3.09 makes the process pretty easy to those who are familiar. This does work even if you have custom Rom and Custom Recovery. Both of which will be destructively replaced by the new firmware. So take a Nandroid!!! Those with Stock firmware UVUEMJC, please take a Titanium Backup of all the essential stuff to external SD. You have been warned.
1. Obtain the Stock update UVUENC2 from SamMobile Link.
2. Download the CF-AutoRoot zip file for D2TMO by @Chainfire.
3. Obtain Odin 3.09 from here. Do not run Odin.
4. Take a backup of important stuff and put the phone in Download Mode.
5. Connect the phone to the PC and let the drivers install if not installed already.
6. Execute Odin as System Admin and then choose the Stock Firmware as AP (AKA PDA in prior versions).
7. Make sure F. Reset Time Option is Checked but Auto Reboot option is unchecked.
8. Complete the Odin flash process.
9 Once that's successful, make sure the phone is still in Download mode.
10. Again Click AP (AKA PDA) and choose the CF-AutoRoot zip previously downloaded.
11. Make sure F. Reset Time Option is Checked but Auto Reboot option is unchecked.
12. Complete the Odin Flash process.
13. When it is successful, Disconncect the phone and pull the Battery. Boot the phone to Stock Recovery and wipe Cache as well as Dalvik if there's an option for Dalvik. (My Phone does not have stock so don't remember)
14. Let the phone boot normally and enjoy Rooted Stock update. Profit !
You can use Root Checker App from Play store to confirm Root. If for some reason it failed, update the binaries of the Super user app. Upon launching that app, it may prompt for the same.
CREDIT - Nasirtech Tutorial from over here.