Give your users an In-Place Archive, so they can keep all their important data in one place. Keep your inbox clean by automatically moving old messages to an In-Place Archive. Anywhere access Provide your user with anywhere access to email, calendar, and contacts on all major browsers and across devices. Users can integrate supported versions of Microsoft Outlook to Exchange Online, to be able to use the familiar and rich client interface. Exchange ActiveSync enables mobile phone users to access their email, calendar, contacts, and tasks, and to continue to access this information while they're working offline. Web-client access For web-client access, Outlook on the web provides a premium browser-based experience that matches the look and feel of the full Outlook client. If a mobile device is lost, stolen, or otherwise compromised, you can issue a remote wipe command from the Exchange Server computer or from any Web browser by using Outlook Web App.
Like always. So no excuses there, go configure it! Microsoft has since published an article to further clarify on this here. Because there are some architectural changes in Exchange Outlook clients no longer connect to a server FQDN as they have done in all previous versions of Exchange. Please restart. Now that we have cleared that part, how to actually configure the mailbox?