After Migration the number of messages in Outlook 2013 seem less then expected. (4213973)

1. Start Outlook 2013.
2. Click Account Settings on the File tab, and then click Account Settings.
3. In the Account Settings dialog box, double-click your Microsoft Exchange account on the E-mail tab.
4. In the Change Account dialog box, drag the Mail to keep offline: slider to ALL
5. Click Next.
6. Click OK when advised you have to restart Outlook to complete the configuration change.
7. Click Finish.
8. Restart Outlook.

For more detailed information and additional resolution options have a look at this Microsoft article. 

https://support.microsoft.com/en-us/kb/2733062