The International version of the S3 (the quad core one) does not have an LTE radio and no firmware will fix that.
The USA versions with the dual core Snapdragon have LTE built into that SoC (system on a chip).
Whether or not it actually functions depends on your SIM card and your carrier's network (and your location within that network).
I stumbled across this in my international S3's APN Settings recently.. I am aware that it doesn't have the required antenna, but I still wonder why the APN's bearer menu gives me the option (upon adding new apn) :
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