Default AU KDDI Samsung Galaxy S III SCL-21 4.1.2 Update and Root

Hello. I just wanted to make a quick post for all of the Japanese AU Galaxy S3 owners out there. For those of you who rooted your phones before AU released the Jelly Bean update, you can still update your phone and regain root.
In order to perform the update I followed the guide written by droidgator at http://www.droidgator.com/update-gal...bmk1-firmware/
However I did find a few discrepancies with his guide and made the following changes:
After Completing step 1 of the guide I then had to press the volume up bottom to get in to the download mode.
Step 2 refers to "an ID:COM box with a yellow color" mine was blue.
Step 3 was hazy and a lot of the information did not apply. Basically all I did was click on the PDA button and load up the md5 firmware file and disregarded the rest of the step.
Step 3: Says to ensure the Re-partition box is checked but since we are not using a PIT file I disregarded this and only checked the F. Reset Time and Auto Reboot.

After hitting start my phone restarted a couple of times and when all was said and done, my phone was updated and I didn't lose any of my information. My CWM recovery and superuser binaries did disappear though, as one would imagine, and after trying several universal 4.12 rooting methods finally had success with re-using the original root method that works for the original 4.0.1 firmware.
The root method I used was made for the firmware 4.0.1 but I was able to successfully root my 4.1.2 firmware using the same method.
The method can be seen at
http://www.youtube.com/watch?v=DouktjBrS5w

I did not created the original tutorial that I used at droidgator nor did I make the youtube video or the root method and big thanks goes to them for helping me to get things done.