There is a good solution to this, usually, but you need to have your original Windows Install disk. Once the swap is made, you boot from the Windows Install disk and choose to do a REPAIR INSTALL, not a normal one. A Repair Install will search through your new hardware and identify, then install all the device drivers it needs (for devices that are built into your new mobo). That can solve most problems caused by missing or incorrect drivers.
The other thing that can happen is that Windows detects such significant changes in hardware that it believes you tried to install it illegally on second computer, and it warns you about this. If you get that kind of message you have to phone Microsoft Tech Support and discuss with them. No doubt they will want to be sure you have a legit Windows Install, etc. If they are convinced that you just had to replace a mobo for any good reason, they will help you re-authorize your Windows.