Android 4.3 Arrives on the T-Mobile Galaxy S III T999 :-
The T-Mobile Galaxy S III was one of these devices until yesterday, when it finally received its official Android 4.3 Jelly Bean update.
The update comes in the form of build ID UVUENC2, it will update your Android version to 4.3. According to T-Mobile support documents, this 37 MB update is available both via OTA and through Samsung Kies. But if you intend on updating through either of the above methods, you can’t be rooted, and you must have at least 50% battery.