You may want to disassociate Office from the old system first if you are able so you can free up a license since you are only allowed to have so many systems installed with a license key and sometimes this is tracked by Microsoft depending on the version.
Manually copying or even migrating using Migration/Setup Assistant doesn't seem to transfer the Microsoft license. Sometimes cloning the entire drive will keep the activation alive. The last couple of times I assisted someone after a drive upgrade, we were unable to reactive Office 2011 even when using the original product activation key. Also the online activation did not work due to "server" issues. I had downloaded the software direct from Microsoft for reinstall. I left it to the user to contact Microsoft or to purchase a newer version of Office to resolve the issue.