Bluetooth keyboard on bootcamp

I'm facing an issue with a bluetooth keyboard on bootcamp Windows 10 Enterprise.

The bluetooth works with all my devices, including the keyboard itself - but to make the keyboard work I must first boot up the MBP Mid 2014 on MacOS High Sierra, make sure the keyboard is connected by typing my password on logon screen and then restart the machine on the bootcamp partition. I don't even need to log-in MacOS, just start typing my password and click on "restart" button. After that, my bluetooth keyboard works on Windows.

It may worth saying that I use two of this keyboards (they are the same-ish Microsoft Mobile Keyboard), and I have the same issue with both.

The same is not necessary with my bluetooth mouse - it has 3 bluetooth channels so that I just need to select the right one.

What should I do to make both keyboards work on Windows without being necessary to launch MacOS first?