While we’re expect Samsung to start releasing Jelly Bean update for their Galaxy S III models sometime after their August 29th Unpacked event, we haven’t seen a lot in the way of official carrier updates leak out, especially for T-Mobile.
This leaked build, JRO03L, is nearly finished but still has a few issues, mainly the inability to use Wi-Fi calling and that’s likely due to this file originating from Samsung and not T-Mobile. We first noticed the file hanging around on SamMobile’s website earlier this morning, but now an XDA-Developer thread is filled with folks installing the file.
One major warning before considering installation: You need to be running the stock build T999UVALH2 before attempting to install, which can be downloaded if need be. Otherwise the installation seems pretty straightforward with applying the Zip in your Recovery menu and then enjoying Android 4.1.1 Jelly Bean.
Disclaimer: Before considering using this, make sure you’re comfortable with the loss of your warranty and be completely familiar with everything involving rooting and recovery.