Hi,
I had my laptop repaired w/ replacing of CPU. After recieving of the laptop I found out that bad guys put wrong version of BIOS. It appeared to be LA version w/ integrated video and it should be LJ version w/ a discrete one. As a result I cannot see the discrete card in a Device manager. For sure, there is no use to install a correct LJ version because of "wrong" version. Is it possible to modify factory UEFI AMI BIOS somehow to make it possible flashed w/o desoldering of a chip?

You should use AFU under pure DOS environment forcing the flash of the whole bios region.

Should I rename .cap file to .rom or .bin then?
Ok, used UEFI Tool.
How do I know the version of Aptio to download correct version of AFUDOS?

@Whatt - You will have to try many versions of AFUDOS until you find one that works, knowing APTIO version doesn't really help much, and some AFU will look like it flashes but really doesn't (not trustworthy program) Sending a PM, all DOS ones I have
Due to the situation, and this being a laptop so I doubt you have a service jumper, it's unlikely you can easily flash another BIOS version due to system ID / BIOS ID will be mismatch, and

You wont have to solder, but I think you will need flash programmer (Like CH341A) and SOIC8 test clip cable to fix this, both together cost around $6 total shipped on ebay, let me know if you need links.
Delivery will take 3-5 weeks, unless you find locally from somewhere for more $$, or China seller that ships faster for more $$. Or you can take it back to where they screwed it up and have them put on the correct BIOS, they should be able to do for you on the spot, it only takes about 2 minutes with a programmer.
Replacing CPU they shouldn't have messed with the BIOS, it's more likely they just swapped out your board/CPU combo for another board that was already flashed or is already this other system.

You can do "Pinmod" to unlock FD, and then you can flash in mismatched BIOS via FPT, see section E1 here
[Guide] Unlock Intel Flash Descriptor Read/Write Access Permissions for SPI Servicing

No matter what you are doing, with any tools, do not rename .cap BIOS to .rom or .bin, that isn't a thing. You need to extract rom/bin body from capsule, which sounds like you've done already, mentioning for others reading in the future

@Lost_N_BIOS - Actually I would get my laptop back to repair shop, but it's located far from my native town. And it's gonna be chargeable enough. That's why I started to solve this problem by myself. During last several days I read different forums regarding BIOS and programmers. I have a USBASP v2.0 available and spent some time to make it fit for SPI flashing. It's not a big deal to order SOIC-8 test clips at Ali but it'll take a month at least while shipping from China. So I was very close to force flash of correct BIOS (image body) through AFUDOS by @Sylar76's advice, but defective Transcend USB flash made my plans crashed )).
Then I begin to study "pinmod" method.

@Whatt - I understand about the shop being far away, it's too bad. Pinmod method will work if you can get it done, but you need to do each time you boot up unless you flash in an unlocked FD right after that first boot.
First download matching ME System tools package for your ME FW version (visible on main BIOS page, or use HWINFO64 in large window on left, motherboard section), from this thread in section "C"
Intel Management Engine: Drivers, Firmware & System Tools

Then do pinmod. Then inside above download you will find Flash Programming Tool folder, and inside that Win/Win32 folder, select that folder, hold shift and press right click, choose open command window here
Run the following commands to #1 test pinmod = success or not and #2 to dump FD so you can edit it.
1. FPTw.exe -d bios.bin
2. FPTw.exe -desc -d fd.bin

If #1 goes without error, and dumps full BIOS, then pinmod success, don't reboot yet until you do next steps.
To unlock the FD.bin created above, follow the steps you see in this thread, section "B" spoiler #2 (use image that matches how your FD looks in hex)
[Guide] Unlock Intel Flash Descriptor Read/Write Access Permissions for SPI Servicing

Once unlocked FD edit is done, save the file, then go back to command window opened above and enter the following command to flash back in the unlocked FD (Then you can reboot, all done)
FPTw.exe -desc -f FD.bin

Then you can reboot, and use FPT now to reflash BIOS region of board you want to use via command below
FPTw.exe -bios -f filename.bin

Be sure you DO NOT use encapsulated BIOS, open file you plan to use in UEFITool first, if you see Aptio Capsule right click on it without expanding and choose extract body, that is the file you use with FPT.

You may need to still unlock "BIOS Lock" before you can flash in the BIOS region, this can be done anytime before or after Pinmod/FD unlock etc.
Here is my guide on how to do that, unlock SMI lock too if you see it in your IFR, it would be right in same immediate area as BIOS lock
[GUIDE] Grub Fix Intel FPT Error 368 - BIOS Lock Asus/Other Mod BIOS Flash
Alt boot to grub when no boot to EFI on exit page - [Help needed] Hidden Advanced menu Bios HP Z1 J52_0274.BIN (2)

@Lost_N_BIOS
Appreciate very much for such a detailed procedure. First of all, I could not find datasheet for my ALC3236 regarding correct pins to be shorted. But the main reason of not doing "pinmod" appeared to be that the audio codec chip itself and surrounding components were too tiny for hook up. Really tiny with my not good visual acuity.
To cut a long story short, I soldered out BIOS, flashed it w/ original dump that I succedeed to find and voila! I got it working finally. Just for educational purposes I'm about to find out more regarding ME regions, etc.

@Whatt - Yes, usually you cannot hook anything up to this chip, it's QFP64 or QFP48 usually (Quad flat pack), no pins on sides. You short the traces there, with needle tweezer or bent/modified safety pin etc.
Good you were able to desolder and solder back without issue, nice it's all running again! You should have unlocked your FD while you had the BIOS out!