Apply zip over STOCK T999UVALH2 found here
Stock firmware T999UVALH2
1. Download and install stock (if you are not already on stock rom) This is needed as a base. The update will otherwise fail
2. Download OTA
3. Apply zip in recovery menu
4. Enjoy Jelly Bean 4.1.1
Since I dont have this model myself, the OTA update is not tested by me.
Please use this at your own risk.
If you want anthing to be added to the post, please PM me.