Excel or PowerPoint error: "This file cannot be saved because some properties are missing or invalid"

Symptoms

When you try to use Save As to save an Excel or PowerPoint file to a SharePoint or OneDrive location, you encounter the following error:

This file cannot be saved because some properties are missing or invalid.

If you select File and then Info, you see the required lookup property that the error refers to, but selecting Show details next to the property doesn't do anything.

Cause

The issue is a design limitation of Excel and PowerPoint.

Workaround

Save the file to your device, then upload the document to SharePoint using the SharePoint web user interface. This operation allows the lookup property to be set. If you open the file later, Show details will allow you to set the property.