There are a few ways to resolve the issue: One option is to remove the recent update that has been pushed out by Microsoft to Outlook 2013 and Office 365 users.
To do so, complete the following steps: Be sure to back up any existing emails or transfer to an offline location before making this change.
The information you enter here will appear in your organization’s address book.
Thus, your Inbox will appear to have a set of missing emails. The problem is that IOS Apple Mail hasn't "fetched" those gap emails yet and therefore is not showing them in your other email clients on the face of the planet (including Apple OSX Mail) fetch from your mail server by latest arrivals first instead of most recently copied or moved.
Or fetch them all, which avoids the problem as well.1.
For more information, see Keep your PC update to date and Update Mail and Calendar for Windows 10.
Once you've updated Windows 10 and the Mail and Calendar apps, If you're still experiencing sync issues, choose your specific problem to jump right to a set of steps to fix the issues.
Older versions of i OS Mail (earlier than IOS 8) showed a "Load More Messages" button at the bottom of the list. Repeatedly scrolling down (or clicking the "Load More Messages" button) will make the app fetch the next batch of messages.