Samsung Galaxy S 3 LTE (GT-I9305) Firmware Overview
What is the latest GT-I9305 firmware?
I9305XXUFQG1, released August 7, 2017 for region FTM with Android 4.4.4. The archive holds 2 official builds for this region.
Is the Samsung Galaxy S 3 LTE still getting updates?
Most likely not: there has been no new firmware since August 2017, so Android 4.4.4 is the last version this model got. The final builds below are still the best choice for a clean reinstall.
GT-I9305 firmware for region FTM
How to Flash GT-I9305 Firmware
Put the Samsung Galaxy S 3 LTE into Download Mode, load the BL, AP, CP and CSC files into Odin on a Windows PC and press Start. Use HOME_CSC to keep your data, CSC for a full wipe.