Each time an account is linked to the Windows installation, a registry entry is set, but it is not deleted when you link a new account to the Windows installation. This registry entry has to be removed by hand. To do so press the Windows key + R, type “regedit” and press enter. Here you have to navigate to HKEY_USERS -> $ID of your Windows User$ -> Software -> Microsoft -> Office -> 16.0 -> Common -> Identity -> Identities. In here you will find an entry with a seemingly random name. Search them all for an entry that contains the email address of your old Microsoft subscription account and delete it.
Most of the times after this the installation should work. Sometimes you also have to uninstall Office entirely and reinstall it.

Microsoft Office 365 Abo from TU Wien

TU Wien offers software for students. One software is a Microsoft Office 365 subscription for students to a good price. For this subscription, you receive a Microsoft account to login and download the software you need. After one year this subscription expires and you have to buy a new subscription and receive a new Microsoft account login. When I bought the subscription for the second year, the account on my Windows 8 notebook was not updated to the new credentials, even after multiple successful login attempts. I could not use the Microsoft Office, because it still ran on my old expired account.
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