T-Mobile Delivering Android 4.1 Jelly Bean to Galaxy S III
T-Mobile GS3 now has LTE support with JB update
After I got the update I checked 
in the mobile network settings it has LTE/GSM/WCDMA (Auto mode) so I contacted Samsung support and they said this update does support LTE. 
UPDATE: I just did a online chat with Samsung support through it's website and they confirmed the this new update does support LTE please see below.
Please wait for a Samsung Agent to respond.
You are now chatting with 'Mikayla'. There will be a brief survey at the end of our chat to share feedback on my performance today.
Your Issue ID for this chat is LTK56402017979X
Mikayla: Hi, thank you for contacting Samsung Technical Support. How may I help you today?
Mikayla: We have not heard from you. Do you wish to continue the chat?
Visitor: Hi Mikayla! I just recently updated my GS3 to 4.1.1 and a noticed a new setting in the mobile networks setting it show LTE/GSM/WCDMA (Auto mode) my question is does this phone support LTE on T-Mobile's LTE network when it's available next year.
Mikayla: I'll be glad to assist you in this regard.
Visitor: thank you
Mikayla: Yes, you are correct. I would like to inform you that your device will support LTE network.
Mikayla: The devices with Jelly bean firmware will support LTE network access.
Mikayla: Please let me know if you have any questions.
Visitor: No more questions, thanks for your help.
Mikayla: You are welcome.
Mikayla: It was a pleasure assisting you. Thank you for contacting Samsung Technical Support. If you have a minute, please click on the blue “X close” button to receive a transcript of your chat and fill out a brief survey to help us serve you better. Have a wonderful day!
Chat session has been terminated by the Samsung Agent.
in the mobile network settings it has LTE/GSM/WCDMA (Auto mode) so I contacted Samsung support and they said this update does support LTE. UPDATE: I just did a online chat with Samsung support through it's website and they confirmed the this new update does support LTE please see below.
Please wait for a Samsung Agent to respond.
You are now chatting with 'Mikayla'. There will be a brief survey at the end of our chat to share feedback on my performance today.
Your Issue ID for this chat is LTK56402017979X
Mikayla: Hi, thank you for contacting Samsung Technical Support. How may I help you today?
Mikayla: We have not heard from you. Do you wish to continue the chat?
Visitor: Hi Mikayla! I just recently updated my GS3 to 4.1.1 and a noticed a new setting in the mobile networks setting it show LTE/GSM/WCDMA (Auto mode) my question is does this phone support LTE on T-Mobile's LTE network when it's available next year.
Mikayla: I'll be glad to assist you in this regard.
Visitor: thank you
Mikayla: Yes, you are correct. I would like to inform you that your device will support LTE network.
Mikayla: The devices with Jelly bean firmware will support LTE network access.
Mikayla: Please let me know if you have any questions.
Visitor: No more questions, thanks for your help.
Mikayla: You are welcome.
Mikayla: It was a pleasure assisting you. Thank you for contacting Samsung Technical Support. If you have a minute, please click on the blue “X close” button to receive a transcript of your chat and fill out a brief survey to help us serve you better. Have a wonderful day!
Chat session has been terminated by the Samsung Agent.
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