Samsung started rolling out the official Android 4.1.1 Jelly Bean update for Samsung Galaxy SIII. Many of the Samsung galaxy S III users have reported about updating Android 4.1.1 Jelly Bean for their device, in Canada. The update is offered on number of carriers and is also accessible via Samsung Kies updating tool.
It is now available for the entire users across the air. You can check its availability for your device in settings menu.