
Samsung GALAXY S4
The latest firmware for Samsung GALAXY S4 (SHV-E330L) is E330LKLUDPI2 with Android 5.0.1, released on September 19, 2016 for 1 region (CSC). Every official firmware build for SHV-E330L, newest first: one row per build with all regions (CSC) that received it.
Each firmware build has its own page at https://samfirm.shop/build/{PDA}, where {PDA} is the build number from the list above. Example: https://samfirm.shop/build/E330LKLUDPI2

SHV-E500L

SHV-E400K

SHV-E370K

SHV-E330K

SHV-E310L
You can find the firmware on the model: SHV-E330L page.
Yes, all firmware files for SHV-E330L are 100% official, original, and obtained directly from Samsung servers.
To flash SHV-E330L, you need to download the appropriate firmware, put your device into Download Mode, and use the Odin tool to load the BL, AP, CP, and CSC files.
Downgrading is only possible if the bootloader version (binary bit) of the old firmware matches the current one. Always check the binary version before flashing SHV-E330L.