The system update process to Jelly Bean (Android 4.1.1 & 4.1.2) is fairly straight forward and depending on your network speed can be completed in under half an hour.
Caution: Before upgrading your phone it is always recommended that you backup your data.
To update your Galaxy S3 phone to Android 4.1.1 & 4.1.2:
- Click on the “Menu” (left) button and Select “Settings” from the popup menu
- Click on “Application Manager”
- Select the “All” view to see all running applications
- Click on “Google Services Framework”
- Click the “Clear Data” button
- Click the “Force Stop” button
- Open “Menu>Settings” again
- Click on the “System Update” option
- Click on the “Update Samsung Software”
BAAM it’s done! In a little under a half hour you will have the 348MB (4.1.1)/157.6MB (4.1.2) download and it will automatically install after a reboot.
Disclaimer: Use at your own risk.