I've did some digging, and this appears to be the easiest and most current method. The others may work, but this is confirmed good with VRBMB1 Jelly Bean 4.1.2. Hope this helps.
How To Root ANY Samsung Galaxy S3 4.1.2 & 4.1.1 ? Verizon/AT&T/Sprint/T-mobile/I9300 Version ? Phone Rebel
ive got a question, I just unrooted my sons vzw gs3. in the instructions it says to reset the flash counter, then flash the bootchain via odin, then the stock rom via odin.
I used triange away and it was successful, then i flashed the bootchain via odin and it was successful also ( i unchecked auto reboot and f reset so that i could flash the rom right after the boot chain. Then i tried to flash the rom via odin and it locked up on me. I rebooted into download mode and it finally flashed the rom. the phone is up and running again but when it reboots i see the little unlocked symbol.
how do i relock it? it is obvious that its been tampered with.
bro, you dont even want to go there. cause once you lock the boot loader then yer up crap creek and no paddle.. sure you will gets OTA updates to 4.1.2 but its about worthless. If you lock boot chain you cant do anything much and even then the phone may lock up (bricked) nothing but a piece of junk.. but there is a place to go to rework the phone like it had come ooutta the box.. then yer in over yer head as there isnt any up to date stuff for the 4.1.2 no root, no recovery, and apparently no one gives a crap.. that where i am now.. oh be sure if ya brick it bad.. just go to odin right click and run as administrator.. to get back where you are or beyond. trust me theres not much out there for a 4.1.2 >>> for the 4.2.2 seems to be on the rise and 4.1.2 left in the dust. heres the one file you will have to odin to get outta the brick when you get there .welp i cant paste it but its there look for GEEK and the fix is there.. all of this a taste of the crap I am going through right now...
Get error404 on the very first download link (the samsung driver). I didn't make it very far at all.