Samsung had officially ended the Marshmallow journey of Galaxy S4 but the phone is not ill-fated at all. Galaxy S4 LTE with model number I9505 can still be updated to Android 6.0.1 Marshmallow.
Samsung Galaxy S4 LTE can still experience Android 6.0.1 Marshmallow via custom firmware based on Android Open Source Project (AOSP). Since it is AOSP-based, there is nothing fancy to expect from the ROM. However, Galaxy S4 owners can rest assured that it is fast, smooth and stable which is the point of ROMs after all.
Team Android warned that the custom firmware is still in its testing phase which will more likely render some of the features unreliable as for now. For those who would want to have the firmware installed, here are a few reminders:
1. Do not use the ROM to other devices.
2. Install TWRP Recovery on the phone here.
3. Back up all necessary data here or via Samsung KIES.
4. Download a driver here.
5. Installing any custom ROM including this one induces risk of damaging device. Neither this site nor developers of the firmware will be held responsible for such damage.
To begin with the installation of the firmware on Samsung Galaxy S4 LTE I9505, here's a step-by-step guide:
1. Download Android 6.0.1 custom firmware here for HTC One M8 on PC.
2. Download Google Apps Package here.
3. Connect phone to PC using the USB cable.
4. Copy then paste downloaded ROM files to phone's memory or SD card.
5. Copy then paste the boot.img file to android-sdk-windowsplatform-tools directory.
6. Switch off phone and plug it out from the PC.
7. Go to Recovery mode by press holding volume up and power buttons.
8. Choose 'Wipe' to delete of data then 'Swipe to Factory Reset'.
9. Go to main menu and choose 'Install'. Choose the copied ZIP file on the phone.
10. Choose 'Swipe to Confirm Flash'.
11. Wait for the installation to complete.
12. Repeat the process beginning #2 for Google Apps.
13. When phone gets into any boot loops or other troubles, tap 'Wipe cache/dalvik' button.
14. Choose 'Reboot System'.
To check for the update, go to Settings > About phone.