Samsung has official releases Android 4.1.2 firmware to Galaxy S3 I9305 users. You can check and get update through Samsung Kies application and OTA update. If you still not get any update notifications, you can try manually download the firmware and flash into your galaxy S3 via Odin application.
If you want to get root access on your Android Galaxy S3 I9305 that running Android 4.1.2 I9305XXBLL3, then below is the tutorial for your reference:
Note: Manually flash firmware into Galaxy S3 via Odin will void the phone warranty. So, take it on your own risk.
Step 1: Download the CF-Auto-Root, then unzip the file.
Step 2: On your computer- desktop or laptop, Open Odin 3.04 (Download Odin).
Step 3: Turn off your phone and then turn your phone in download mode by press (Home+power+vol down) button.
Step 4: Connect phone to the computer and wait until you get a yellow sign in Odin.
Step 5: Add CF-Auto-Root-m3-m3zh-gti9305(.md5) to PDA.
Step 6: Start flash, sit back and wait a few seconds.
Step 7: Galaxy S3 will automatically reboot once the CF-Auto-Root file complete flash into your Galaxy S3SI9305.
That’s all!
