I can not update the BIOS F.50 to F.56

[StrelokVC]

Through the search page for my laptop (https://support.hp.com/ru-ru) I went to the software download page and saw that there is a newer bios version F.56 (I have F.50 installed)
I downloaded a new bios, ran the installer, but he told me: "The BIOS update is not compatible with this device."

I couldn't get him to update my BIOS in any way. The serial number of my motherboard is [personal information removed] and here I have doubts.
Several years ago my motherboard was replaced under warranty in Russia, Moscow. And before this replacement, I had the serial number [Personal Information Removed] (the last two letters have been changed). Perhaps this is a mistake of the technicians who updated my data on a new, replaced motherboard. It seems to me that the problem in updating my BIOS is precisely in this problem.
How can I update my BIOS?

[Huffer]

Have you tried one of the interim new BIOS issues. I see the download page has an F.52 and an F.53. Normally you can go from any prior version to the newest but sometimes it can help to do it in 2 steps. If you run HP Support Assistant does it accurately report your model and serial number? If so the motherboard was correctly re-tattooed by the technicians in Russia. 

[StrelokVC]

Unfortunately, on the download page, I have only one BIOS available, F.56. Intermediate versions 52 and 53 are not visible to me. Am I looking somewhere in the wrong place? Please give a link to these intermediate BIOS versions.

In HP Support Assistance, I have two laptops after repair. The one that was before the repair and the one after. They are displayed with the same model, but with different serial numbers, as I wrote above.

[Huffer]

Here is the page:

OMEN by HP 17-w100 Laptop PC series Software and Driver Downloads | HP® Customer Support

Here is F.52:

https://ftp.hp.com/pub/softpaq/sp96501-97000/sp96552.exe

Open up the BIOS and look for a link to previous versions. So to be clear the 2 screenshots you posted are the same laptop....one before and one after the motherboard replacement? Had HP done the replacement the techs would have tattooed the motherboard with your original serial number. Not sure how that affects the ability to update the BIOS. If it were not a genuine HP board the Support Assistant would not detect it as such. 

[StrelokVC]

Yes, you understood correctly. Above, two screenshots are the same laptop, but one screenshot is before repair, and the second screenshot is after repair (there was a replacement of the motherboard under the official HP guarantee).

So, I downloaded all the updates after version 50 and updated one by one in the following order: 50 -> 52 -> 53 -> 55. But the last update 56 is still not installed. I'll attach a screenshot of this window, maybe I'm doing something wrong again?

sp111733.exe

PS. I was trying to create a bootable USB drive as the installer suggests. But how to update the system from this disk, I don't understand. After the reboot, the windows are loaded immediately. The system does not ask any additional questions about the update.

[Huffer]

You can copy the BIOS image to a location on the hard drive (last option) and then use the UEFI BIOS upgrade tool by tapping esc as you power up then F2 then find the BIOS update. It will let you browse the hard drive for the location of the BIOS image. This usually works even when other methods fail. At least we got you up to F55, right?

[StrelokVC]

Yes, thank you very much! As I wrote above, I have already upgraded to F.55 with your help.

Now I followed your advice and saved the BIOS to the C:\. Then I rebooted and, without waiting for the operating system to load, I pressed ESC. I have already seen this menu and covered everything here, now I will show it to you:

Startup Menu

As you suggested, I pressed F2 and went to the additional menu, in which there are only a couple of tests, but no mention of updating the BIOS.

HP PC Hardware Diagnostics UEFI

And finally, one more screenshot of information on my system. Here, too, I did not find any opportunities to update my BIOS.

[StrelokVC]

I have some successes, now I will tell about them.

On the product page, in the Advisories section, I found the release notes for HP PCs - HP PC Hardware Diagnostics (UEFI) Version 7.6.0.0. Here is the link https://support.hp.com/us-en/product/omen-by-hp-17-w100-laptop-pc-series/12499486/model/13222216/doc...
I downloaded this package and installed it. And after rebooting, I again went into the diagnostic system by pressing the F2 key and saw another HP menu with a lot of tests and also the BIOS update function.

I was very pleased with this success and tried to continue to act according to your recommendations. I found unpacked firmware dumps and then I got stuck. There are 3 of them. Which one should I choose to upgrade? When I select each of them, I see that it is version F.56, but there are no more details. Which of these files should I flash into my BIOS?

BIOS utility interface

[Huffer]

The highest number in this case 0820D.bin. This might be one of the BIOS you have already installed, but worth a try

[StrelokVC]

On your recommendation, I tried the file you suggest. I get the message "BIOS Image file specified is not intended for this system". I tried all three files in turn. When trying to flash each of them, the utility reports the same thing.

What are we doing wrong?
How can I flash BIOS version 56?