
Samsung Galaxy S 2 HD LTE
The latest firmware for Samsung Galaxy S 2 HD LTE (SGH-I757M) is I757MUGMC5 with Jelly(Android Bean), released on March 28, 2013 for 2 regions (CSC). Every official firmware build for SGH-I757M, 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/I757MUGMC5
The newest build, I757MUGMC5, was released on March 28, 2013. No new build has appeared for 165 months, so regular updates for this model have most likely ended.

SGH-I927

SGH-S730M

SGH-T999N

SGH-T989D

SGH-T859

SGH-T599V

SGH-I747

SGH-I717R
The latest build for SGH-I757M, I757MUGMC5, was released on March 28, 2013 (13 years ago).
SGH-I757M has had no new firmware for 165 months, so regular updates have most likely ended.
Yes, all firmware files for SGH-I757M are 100% official, original, and obtained directly from Samsung servers.
To flash SGH-I757M, 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 SGH-I757M.