Here's a link to the latest official firmware for the S3 I9300 (release date: Nov. 2013):
http://goo.gl/e7PA04
The XXUGMJ9 is a Jelly Bean 4.3 "No-Wipe" stock ROM which is compatible with previous versions like 4.1 and 4.2.
It is always preferable to back up your EFS folder to restore your IMEI (in case needed) before you proceed if you haven't done that in the past.