Sprint may have been the first to roll out the Android 4.1 update for the Samsung Galaxy S III, but T-Mobile customers can now join in on the party. We’re received a handful of reports that the Jelly Bean update for the T-Mobile Samsung Galaxy S III has started rolling out and T-Mobile has updated its handset support page with details of the new software update.

Android 4.1.1 for the T-Mobile’s Galaxy S III will include Google Now, expandable notifications, Android Beam, automatic widget resizing, camera enhancements, improved Wi-Fi calling and slight tweaks to the keyboard. Of course it won’t be stock Jelly Bean, but Samsung has added some useful features in the latest version of Touchwiz.

If you have not yet received the Android 4.1.1 update on your T-Mobile Samsung Galaxy S III, you can try to manually ping the update server by pressing Menu > Settings > About device > Software update. If that doesn’t work, Samsung has also made the update available through Kies. The manual download and installation takes a bit longer, but it sure beats waiting another week or two for your Jelly Bean update.

Let us know if you have received the update yet and how you like all the new features included in Android 4.1.1.