Flashing different latpop with my BIOS - HP DV6-2056el to DV6-1044el

[amedeux]

I'm not sure if the title is clear.
I have 2 HP laptops DV6-2056el and DV6-2044el. I want to fix some DV6-2044el fan poblems (it fires up and stays at max speed forever) using a dedicated BIOS update from the DV6-2056el.

Both laptops have same exact Mainboard model, Insyde Setup Utility Revision (INSYDE EFI rev 3.5), Chipset, CPU, ram type, Graphic Board (same revision here, too) and same chassis too, of course.

A side to side comparison of the first bios screenshot suggest we're indeed talking of the same thing:
Bios Screenshot Comparison

Same for CPU-Z:
CPU-Z Comparison

Here you can find all the bios screenshots.
2056el:
Bios Screenshot 1
Bios Screenshot 2
Bios Screenshot 3
Bios Screenshot 4
Bios Screenshot 5
Bios Screenshot 6
System Info

2044el:
Bios Screenshot 1
Bios Screenshot 2
Bios Screenshot 3
Bios Screenshot 4
Bios Screenshot 5
Bios Screenshot 6
System Info

Do you see any reason to advice me against that? Is there anything I'm missing?
Thank you ever so much for any advice you could give me!