Before you could do a System Upgrade in your rooted Samsung Galaxy S4 T-Mobile you have to Unroot it, otherwise it will tell you that your "firmware has been modified in an unauthorized way"
This happened to me when i wanted to upgrade mine and i sorted for a way to unroot it and i was surprise to see that all unrooting apps on the playstore (i only saw 2) were paid app.
Now, how could you root a phone for free and when you wanna unroot it, you have to pay ?
So i rooted my Samsung Galaxy S4 T-Mobile with Kingroot, and when i recently updated Kinguser, i discovered that it has a new option to fully unroot your Samsung Galaxy S4 T-Mobile but System Upgrades will still detect your device as a "Modified Firmware"
So a lasting solution is is to flash a new Stock Rom and i will solve your problem as it did to mine.
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HOW TO UNROOT SAMSUNG GALAXY S4 T-MOBILE
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2. Download the firmware meant for your device HERE
3. Extract both the downloaded file to your desktop
4. Double click on Odin and it should launch
5. Click on PDA and choose the stock firmware you downloaded earlier
6. Make sure RePartition is unchecked if checked
7. Check the Auto Reboot box and F.Reset Time
8. Switch off your Samsung Galaxy S4 T-Mobile
9. Switch it back on by pressing VOLUME DOWN+HOME+POWER Buttons together
10. Press volume Up and your phone should enter Download mode
11. Plug in your Samsung Galaxy S4 T-Mobile to your PC with a USB cable
12. Press Start and Odin will start flashing the stock firmware this will take like 5mins
13. Once done, your Samsung Galaxy S4 T-Mobile will reboot
14. You're done.
Now you are done, Its pretty neat and simple
Now head on to System Updates and update your Samsung Galaxy S4 T-Mobile
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