The H-Factor

This is a 're-reprint' due to the fact that this now seems to be an issue:

How do you authorize a seat of AutoCAD that has moved from one machine to another?

Autodesk has an FAQ on this: License Transfer Utility

This can be done with the License Transfer Utility found by picking Start, Programs, Autodesk, [Autodesk Product Name], Portable License Utility.

You can then remove the license from one computer and put it on another.