The issue here was that the Office 2013 (365 edition) on the PC was originally registered under the account of USER A, which was removed in Office 365. So the new user using the PC now, USER B, was getting a warning that Office had to be reactivate d.

Change the subscription account for Office 365 ProPlus | Manage Office 365 | Microsoft Office 365 Community by doing the following.

1. Open Command Prompt

2. Run command to display the license status: cscript ospp.vbs /dstatus

3. Note the last five characters of any and all license keys that display in the output: 

4. Now run the following command as many times as needed to remove all of the license keys you noted from the previous step: cscript ospp.vbs /unpkey:<last five characters of product key> 

5. Once the remove commands are successful, close the command prompt and restart the PC.

6. Launch one of the MS Office 2013 applications (Like Word). The application should prompt you to reactivate by providing your sign-on ID. Enter in the USER B's credentials and the software will now be licensed under their ID.