Updating P13REU bios with a .cap file?

I have this laptop, a Samsung Expert NP350XBE-XD1BR, with an American Megatrends Inc. BIOS, which I want to update. I was unable to find a way to extract its current BIOS, and Samsung no longer officially provides them through its website. Still, I managed to find a way to download the .exe file for the current version of the BIOS, but when I ran it, it failed to update, despite me running it several times, including in compatibility mode (without doing that, it only restarts rather than trying to update, but either way, the BIOS doesn’t change).

As a last resort, I extracted the files contained in the .exe, leading me to find a .cap file, which is apparently some sort of update file. But it’s not bootable, and all the update guides I’ve found so far were exclusively for updating with bootable media. Maybe I am missing something? Any help would be appreciated.

TLDR; I want to know how to update my computer’s BIOS with the .cap file I extracted from the official firmware

AFUWIN or the Intel ME FPT tool, one or another can make backups…maybe.
CAPSULATED files contain the firmware/update image inside, UEFI tool can extract this image, usually named Intel image or UEFI image.
The thing is, Samsung always… or mostly, uses their own app to download bios update files and not posting direct downloads to it.
Also, many bios update files are not a complete bios, they may lack the ME firmware image, EC and/or only updates the bios region when executed.

Now depending on what we get from Samsung files it may or not be possible to flash as they are. That Samsung CAP can be prepared by them as Recovery file.
Can AFUWIN (version…?) What flash utilities does the Samsung bios have embedded?
Intel FPT can also flash a full image, only bios region or ME FW, if the FD (Flash descriptor is unlocked only)

What’s your current bios version?
Is the P13REU latest bios available for that model?
You can share any files for further analysis, if you want.

EDIT: Did try to execute that Samsung bios update file as CMD line admin, try it.

And dont put lock on your downloads, shared it and stop sharing when you want it.

And where did you confirmed that the P13REU is not latest version?

I will try to share some files with you. Here are the executable and the extracted files:
https://drive.google.com/open?id=10nJAOUWxZV4KF0mhfO7_Llyjt6guQ2vj&usp=drive_fs and https://drive.google.com/open?id=10hmUjAMiS2ODpS5eJwp4AeY2HWTabXLW&usp=drive_fs

I’ll try to run the executable with CMD, please hold for a bit, as it’ll probably take a while.
And to answer some of your other questions, I’m not sure but I know my version of P13REU is not the most up to date one. But if it helps, Samsung Update does not show an option to download a BIOS Update, nor does Windows Update. But I don’t know if that’s because of a quirk of the bios, like something preventing it from receiving updates or if the update just isn’t an option for this model.

Update: The files are open now, please check them. In the meantime, I’ll try running the .exe with cmd.

To answer the version thing, it’s because of the date. My BIOS is P13REU 20220223 (February 23rd of 2022), while the one available for download through Samsung’s website (if you have the right links) is P13REU 20220314 (March 14, 2022). The names are longer, of course, but the relevant information is the date.

I never said the .exe went correctly, how would I know?? If it’s true that it worked correctly, then that’s great, but I wouldn’t be able to tell. I was able to run it, but I thought it didn’t work because the BIOS version didn’t change.

And for the record, when I did it, I ran it with compatibility mode for Windows 7, which also works the same way. Before, it only rebooted the system, didn’t show any EC screen or anything. So even when I ran it “properly”, I thought the fact that it didn’t change the BIOS meant it failed. I had no way to tell.