[T-Mobile, Samsung Galaxy SIII] tonytien:
Hi jaddelc,

You can update to a newer version of Android by installing a custom ROM. One of the most popular custom ROMs is called LineageOS. The T999L is supported under LineageOS, so you can install it on your T999L.

In order to install LineageOS, you will need Odin, a custom recovery, a LineageOS ROM file, and a Google Apps package (if you want Google Apps). Please note that you will need a computer running Microsoft Windows to use Odin.

You might also need to install the Samsung Mobile USB drivers for your computer for Odin to work properly. I haven't personally needed these drivers on a computer running Windows 10, but I'll include the link for the drivers in case you need them.

Keeping this in mind, SGH-T999L is also known as d2ltetmo and sometimes d2tmo (for anything except modem files). Also, keep in mind that by following this, you are performing this at your own risk, your data will be erased, and your warranty will be void! Please back up your data beforehand and follow these directions carefully!

Downloads:

LineageOS downloads for d2tmo

Google Apps from The Open GApps Project

TWRP, a custom recovery, for d2tmo

Odin v3.11.2

Samsung Mobile USB Driver

Procedure

Download the latest version of LineageOS from the link above using your phone.

Do you want Google Apps? Google Apps includes the Google Play Store. If you want Google Apps, go to step 3. If you don't want Google Apps, go to step 4.

Go to The Open GApps Project page on your phone. Select the ARM platform and Android 7.1. For the variant, you have a few options. If you want to choose exactly what Google Apps you want to install, choose the aroma variant. This option, however, has the biggest file size, which may be a problem if you have limited data. Other good options are mini, nano, pico, or micro. The stock and full variants might not work with T999L because Samsung made the system partition too small. Don't choose tvstock; that option is only for Android TV devices.

Download the latest version of TWRP for d2tmo and Odin onto your computer.

Open Odin3_v3.11.2.exe and plug in your phone to your computer. Make sure no other Samsung devices are plugged into your computer. Wait a few moments. Something should appear in one of the boxes under ID:COM. If Odin doesn't show anything in one of the ID:COM boxes, you'll need to install the Samsung Mobile USB drivers before continuing.

In Odin, click on the AP button. A new file picker window will open. Find the TWRP file you download earlier, and double-click it.

Press the Start button in Odin. Once you've clicked start, don't unplug your phone! Wait until Odin says PASS. Your phone will restart. Unplug your phone from your computer.

Turn off your phone. Hold down the volume up, power, and home button keys at the same time until you see blue text at the top left of the screen that says "RECOVERY BOOTING". This step can be tricky when you're doing this for the first time. Click here for a video demonstration if you need help with this.

You should now be in TWRP. Tap Wipe, and slide the slider that says Swipe to Factory Reset. When it is finished, tap Back, then tap the back arrow button.

Tap Install. Tap Select Storage, and make sure Internal Storage is selected. Tap OK.

Scroll down and tap sdcard. Tap Download. You should find the Google Apps package and LineageOS ROM that you downloaded earlier here.

Tap the LineageOS file .zip. Tap Add more Zips. Tap the open_gapps package .zip.

Slide the slider that says Swipe to confirm Flash.

Once it is finished, tap Reboot System. Your phone should now boot into LineageOS.

Please feel free to let me know if you have any questions about this process.