Yeah it's a bit of a hassle, but I enjoy the challenge! 
The experience of the other person who had the same issue, speaking to the Fujitsu engineer in Thailand seemed to be almost open hostility towards the Ubuntu guys.
I'm just happy after using YUMI it was able to load the Windows installer absolutely fine. So I'm hoping it may solve the issue.
I'll definitely report back 
Attaboy 
My understanding was that Fujitsu sold two lines of Lifebook; one with Windows and other with no OS. Apparently this caused an accidental flashing with wrong BIOS and bricked many Lifebook. Fujistu then discontinued no OS version of Lifebook.
While it is not easy to find PC with no OS here in France, consumers can purchase a system with OS (i.e., Windows) and request a de-installation plus refund.
I took an advantage of this programme and shipped Acer Aspire to their service centre - got 25 Euro refund 
The shipping cost was also covered by the manufacturer.
There is a lengthy story and court cases behind this refund programme. I will not go on about it but the information can be easily found by searching in French language.
That's interesting. I noticed that on the other support thread.
Updates!
I reinstalled Windows 10. And managed to (finally) flash the BIOS using Fujitsu's utility.
The newest version 2.09 isn't compatible with BIOS below 2.X (mine is 1.10), and the highest one listed for windows was 1.0.4!
So I tried it anyway, and the tool wouldn't downgrade, so I had to run configure it to skip version checks etc. (that took a while to work out how) and then it blue screen errored TWICE whilst trying to flash it.
I went back to Fujitsu's website and checked under the "Admin" type which includes DOS and Windows versions. And the highest there was 1.08, so I tried that. This used a non GUI utility and didn't seem to care that it was less than version 1.10.
I wonder whether 1.10 was discontinued due to bugs? 
After it flashed successfully and rebooted, BIOS is available again! Huzzah!
I'm currently installing Zorin into the rest of the HDD and will see if it kills the BIOS this time.
Zorin is now installed, and it did indeed kill the BIOS again.
So, I'm going to flash the BIOS a second time and hopefully be done!
I checked Fujitsu site and it is a dog's breakfast 
Extremely difficult to find anything. Fujitsu is a good name for office machine and server market but I've never own their consumer product nor recommended it to anyone.
As for your question about BIOS version, unless BIOS prohibits to flash with older version, it is OK to flash it with any version as long as it is compatible. More recently, for security reasons, newer BIOS let you flash only with same or higher version though.
I keep my fingers crossed that your tactics work.
It is a good thing that you pin pointed the root cause of the problem 
You are doing a great service for anyone who will find this thread in future!
Restoring the BIOS worked, but then this also automatically boots into Windows now. So, I ran boot-repair from my live CD, which let grub2 load again. But now BIOS is lost again!
It seems grub causes the issue here. I'm going to run Windows startup repair now, and then run EasyBCD to boot Zorin via Windows Boot Manager instead of using grub2.
I agree with you 100%. It is way easy to handle Boot options in Windows than Linux and EasyBCD** is my go-for tool.
Windows is not a bad operating system. It is easy to use. It is just lacking security. 
That is why I prefer using VM Windows protected within Linux.
** I just realized that you might be using UEFI mode rather than legacy BIOS. If that is the case, EasyBCD would not work, You need EasyUEFI. It is not a freeware, but there is a free trial period which should be long enough to set the boot order.
I have finally got everything sorted!
That was a marathon. You're right EasyBCD isn't compatible with UEFI. EasyUEFI (Free trial) was excellent for what I needed. After flashing BIOS a couple of times, the boot failed to load the windows boot manager either, so I was left in the grub cli.
So, in the end I needed to perform these additional steps:
Run boot-repair from the Zorin Live USB. (this corrupts BIOS)
Reboot into installed Zorin.
Install rEFInd to replace grub as boot manager.
Reboot into Windows.
Reflash the BIOS using Fujitsu's utility (this fixes BIOS)
When it loads into grub cli, manually boot into windows efi, like this, but replace hd0,gpt1 with the correct partition:
insmod part_gpt
insmod chain
set root=(hd0,gpt1)
chainloader /EFI/Microsoft/Boot/bootmgfw.efi
boot
When Windows loads:
Run EasyUEFI
Click Add Item > Select Linux or other OS > name it rEFInd
Check the partition containing the rEFInd boot loader
Browse to "/EFI/refind/refind_x64.efi" for the file path
Click OK to create the rEFInd entry in BIOS boot options.
Move the entry to the top of the list.
Reboot and you're done!
I now have both a dual booting system with Zorin and Windows AND a BIOS that I can configure and boot from USB sticks 
, seems like such a simple thing at first....
That is a "joy of UEFI" 
I remember (and still own) BIOS only systems where making dualboot is much much simpler.
My husband always making a point to install his OS (MXLinux that is) in a legacy mode just for that reason.