A couple of days ago Sprint started rolling out the Android 4.1.1 Jelly Bean update for its variant of the Galaxy S3. The update is being rolled out via OTA so it will take sometime before the update is available to all Sprint SGS3 owners.
Thankfully, there is a very easy method to manually update the Sprint Galaxy S3 to Jelly Bean without voiding its warranty. The method does not require root access, ODIN and does not even wipe your existing data and apps on the phone.
Step 1: Download the official Jelly Bean OTA update from Google’s server from here. Once the download is completed, transfer it to the SD card of your Sprint Galaxy S3. Make sure you don’t transfer the file inside any folder. Do not rename it.
Step 2: Make sure you are running the latest Ice Cream Sandwich firmware (LI3) available for your handset. Go to Settings -> About Phone and then check the Baseband and Build Number. The last three characters should say LI3.
Step 3: Switch off your Galaxy S3 and restart it into Recovery mode. To boot into recovery mode, press the Volume
down Up + Home + Power button simultaneously. You will see the Samsung logo for a brief moment before the Android stock recovery comes up on the screen.
Step 4: Use the Volume buttons to navigate and select the ‘install update.zip from sdcard’ option. Then, select the file that you had transferred to your phone back in Step 1. Confirm your action by pressing the Power button.
Once the update has been successfully flashed, your phone will automatically reboot. The zip file is pretty big, so the flashing process will take sometime. The first reboot will also take a bit longer than expected so please be patient.