often has some type of filter applied. His folders show a-ok, and the email shows in the web, but not in his local outlook.
https://support.microsoft.com/en-us/help/2530570/items-disappear-or-are-not-visible-in-an-outlook-folder
For Outlook 2010 and later versions In the ribbon, select the View tab. In the Current View area, click View Settings. Click Filter, and then review the following tabs tabs for any selections that could filter out specific messages:
Tasks>More Choices>Advanced
Click on "Clear all" then click "OK" and it solved it for him