The activation resource for Windows 10 has changed from earlier versions. Once you upgrade a system, the information is matched to that configuration, much like an OEM license. In some manner, it is tied to the configuration the upgrade was done on. This is why you can do a clean install without needing a License key after the initial setup.
If you want to move the OS, you probably first have to move Windows 7 and then go through the process again for that configuration. I would assume the move would invalidate the Windows 10 information for the first system.