Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
If you have a retail/perpetual Office Professional Plus 2016 product key, first uninstall Office 2016 from the old computer. Then install Office 2016 on the new computer using the Microsoft account or installation media associated with the license, and activate it with your product key. A retail license normally permits installation on one computer at a time, so transferring it means stopping use on the old computer.
If this is a volume-license copy of Office Professional Plus 2016, the process is different. Professional Plus is commonly distributed through volume licensing, in which case activation may use KMS or MAK rather than a retail product key. You cannot necessarily transfer it simply by entering a product key.
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hth
Marcin