Windows 10 won't boot after installing Ubuntu to a different drive

So, here is my problem:
I tried to install Ubuntu 16.04.3 LTS to an old HDD I have (let's call it HDB) while maintaining my main OS (Windows 10) on my main HDD (let's call it HDA). The problem is that after I installed Ubuntu to HDB my Windows 10 (which was on HDA) wouldn't boot.

Full history to better contextualize:
Before starting the Ubuntu installation process I got a message saying that there were some Windows partitions on HDB, which I found strange since I formatted the drive before (and could boot my Windows 10 just fine), but just to be sure I cancelled the installation, shutted the PC down and removed both SATA and power cables from HDA so it would be impossible for the installer to do any changes on that drive. Then I installed Ubuntu to HDB - still got the message saying there were some windows folders/partitions in it, but I was pretty sure it had nothing to do with my HDA installation - and later on it loaded just fine. So I unplugged HDB's (now with Ubuntu) SATA and power cables from my MOBO and plugged HDA (which should have my Windows 10 installation untouched) back in, but to my surprise Windows 10 wouldn't boot, it was (still is) giving me the "Reboot and Select proper Boot device or Insert Boot Media in selected Boot device and press a key" error.
I looked for help on Ubuntu forums, we tested some things there and came to the conclusion that I somehow either managed to delete my EFI partition on HDA or it was on HDB the whole time and for some reason I was able to boot Windows 10 even with HDB disconnected and/or formatted (which I did before installing Ubuntu).
So I think the question now is: Is it possible (if so, how) to recreate the EFI partition, which possibly never existed on HDA in the first place? I've seen some guides on how to do it, even some 3rd part apps that claim to do it, but I think my problem is quite different of what other people been having, and I don't want to mess it any further.
I ran gpart on a live-usb Ubuntu to see what is the state of my HDDs and here it is:

HDA (sda):

Only shows a "msftres" partition (which is not the OS partition, I guess?) and a "basic data partition". Could Windows 10 installation be on the later?

HDB (sdb):

As expected, only has partitions related to Ubuntu (Linux) installation. If my Windows 10 EFI partition (and maybe others?) was there it was 100% overwritten it seems.

Sorry for the lack of more technical info or if it looks confusing, I’m a just a noob when it comes to IT, I only know how to do some formatting, partitioning, OS installing and know a little of hardware, but that’s all, I have zero programming background. And sorry for any grammar mistake, English is not my first language. Thank you in advance.

No, I didn't. I thought that whatever Windows partition was there was from the old Windows installation I had in that drive a long time ago. I did "look" at it on "Computer" after formatting and it showed as empty (~160GB space), but EFI and other system partitions do not show there, from what I learned today, since they have no letter assigned to them, right?

HI,
Only other partition would be a Fat32 I believe it is about 16mb's it's the boot loader for win-10.

Hi,
Yeah maybe that is for bitlocker ?

Did you or someone else install W7 on HDA, while HDB was hooked up ?

Maybe I installed Windows 10 on HBA while HDB was pluggued, could be the reason why boot files ended up there, but I can't be sure. The strange part is that after Windows 10 was intalled on HBA I am pretty sure that I removed HDB and could boot it with no problem at least once.

So, I just formatted HDB again, converted to GPT and installed a fresh Windows 10 on it, just to be sure I removed the SATA and power cables from HDA again. Installation went perfectly fine, installed MiniTool Partition Wizard, shutted it down, plugged HDA cables back in, booted the new Windows 10 (on HDB), launched MiniTool Partition Wizard and HDA doesn't even show there! It's only getting worse hahaha!
New Windows 10 installation on HDB seems to have every partition at least...

Ok, I set BIOS config to default (I changed boot option to "UEFI only" to load the usb with Windows installer before installing it) and HDAis showing now. I don't know if that was really the problem, but it's showing now and that's one less thing to worry hah.
So, I found some ways to restore the EFI partition, one of them is by using the "Partition Recovery" option in Partition Wizard, or creating it "manually" with DiskPart on Windows PE. The first option seems easier, but is it really safe? Link with the methods: How to Restore Deleted Windows Partition after Windows Can't Boot?
Edit: print