The JellyBean upgrade for the international GALAXY S III has begun over a month ago and it is rolling out in stages in different regions. Just recently Samsung begin massively deploying Android 4.1 upgrades in Europe.
Continuing the JB software upgrades for all GALAXY S3 variants, Samsung Electronics started rolling out this morning on its domestic market an update for the LTE version (SHW-E210S). The update is available through Kies software tool.
Americans will have to wait a little bit longer as Samsung said it will be available by years end. For now Sprint is the only carrier in the US who started rolling out the firmware upgrade.
For more details Korean customers should check the instruction in the source link below.