If you are running a 2010 or 2011 product that includes the License Transfer Utility (LTU) in the start menu for that product, you could try exporting the license before swapping the motherboard. That will deactivate the product. After swapping the motherboard, run the LTU again to import that license back into the product. Being that it is the same product installation on the same hard drive, I'm not 100% certain that this will circumvent the need to activate the product again but it's worth trying. Worse case scenario is that you have request a new activation.
Tom Stoeckel
Autodesk Product Support