When a installation of Windows completes, one of the last things it does is to setup the applications and drivers you need to start the computer. If you take a mass storage device from the computer where the operating system was installed the computer may not be able to start because the settings from the other computer are not compatible with the other computer. But you can get around this by using sysprep.exe to generalize the mass storage device after which you can install it in another computer without complications. Once this is done the operating system will find the needed applications and drivers and assign these for the startup.
If you run sysprep on the HHD/SSD with Windows 8.1 or Windows 10 before using it with another motherboard you should be be able to boot from it without any complications.
Press the windows key
and the X key to open the Windows Mobility Center menu.
Select Command Prompt (Admin.) from the menu. This will open the Command Prompt.
Copy and paste sysprep /generalize /oobe /shutdown in the Command Prompt.
Once you have completed this shut down the computer and do not power the drive back on until it has been installed with the different motherboard.
Note: You'll want to install the new motherboard chipset drivers for the new motherboard after moving the drive.
When the computer is started Windows will search for the needed drivers needed to start Windows.