Hi ArtSalihu,
Sorry for the inconvenience that has been caused.
I would like to confirm if your mail data synchronization on Outlook Web App (OWA) and other clients such as Outlook 2013 on Windows OS is working fine. If yes, the sync issue you’ve been encountering should be related to the specific Outlook for Mac client.
Since our forum mainly focuses on Office 365 Online Services, to ensure you get dedicated assistance, we recommend you post a thread in the Outlook for Mac client forum. Thanks for your understanding.
And if any synchronization issue occurs to OWA or Outlook 2013, please just let us know.
Best Regards,
Allen