This is when it is critical that you have associated all of your devices and their Digital License to your Microsoft Account.
If you do not get this done ahead of needing to re-activate a system the process will not work.
As a reminder, if you already log into Windows 10 in build 14371 or beyond with your Microsoft Account and your device is activated then the info is automatically stored.
If you use a local account with Windows 10 you will need to go to Settings > Update & security > Activation and be sure to sign in with your Microsoft Account to associate that devices Digital License with your account for future use as necessary.