Google today to start putting the update to Android 4.1.2 galaxy s3.
way to install android 4.1.2

Here’s how:

1. 1. Download the firmware GT-I9300XXELKF here
   2. Unzip the file you get. Tar.md5: GT-I9300_XEO_I9300XXELKC_I9300OXXELK4_I9300XXELKC.tar.md5.
   3. Now open Odin v1.85 ( download here ), click PDA, then add the file. tar.md5.
   4. CAUTION:  Make sure the box re-partition is not checked.
   5. Start by putting out your galaxy s3 and put the Download mode. (Simultaneously press the Power button, Home, and Volume Down. When a message appears, confirm by pressing the Volume Up)
   6. Now connected to your PC (via USB cable) and press start.
   7. Let Odin work.
   8. Galaxy s3 will reboot your all alone.