Looks like the Samsung Galaxy Tab Ice Cream Sandwich update parade is continuing, as the T-Mobile version of the Galaxy Tab 10.1 has begun receiving a bump up to Android 4.0.4. The update will bring the Tab 10.1 (SGH-T859) to software version T859UVLH6. It's worth noting that, after the dust settles and this update has been installed, the Tab 10.1's home screen layout will be wiped.
When it comes to actually installing the T-Mobile Tab 10.1's ICS update, T-Mo says in its support document that the update is only available for download using Samsung's Kies computer software. However, several users claim to be receiving it as an over the air update, so T-Mobile Galaxy Tab 10.1 users might want to go into the "About device" section in the device's "Settings" menu and check for the update that way first. If nothing shows up, you can find the necessary download links and instructions at the T-Mobile link below. Happy updating!