Using Odin (download for Odin is included on the page), install this:
[Official] Latest STOCK ROMS for SPRINT SGS3 (SPH-L710) - [24/05/2012 - L710VPALEN] - xda-developers
Then take incremental OTA updates to LG2 (It should go LF9 and then LG2). Or download these to your phone (do not put them in subfolders):
[OTA UPDATE] LG2 update ZIP file - xda-developers
Start with LF9. Put it on the phone (do not have the LG2 file on there, yet). Then turn off your phone. Turn on your phone by holding Vol UP, Home, and Power. Stock recovery will flash the LF9 update. Boot back into Android, delete the LF9 file and put the LG2 file on there. Turn off the phone and repeat the update process. You're now on LG2 again.