If you do not have access to the Exchange infrastructure, you can export the emails to a PST file or to a CAB file.
From the navigation pane, go to Protect > Applications > Office 365.
The Office 365 apps page appears.
In the App name column, click the app that contains the item that you want to export.
The app page appears.
On the Mailboxes tab, select the mailbox that contains the item that you want to export, click Restore, and then click Restore messages.
The mailbox contents appear.
Select the item that you want to export.
Click Export selected items to, and then click PST or CAB.
The Export dialog box appears.
In the Name box, type the name of the file that you are exporting.
Note: You can export the mailbox to CAB in either EML or MSG file format.
To view the exported mailbox, on the app page, click View exports.
The View exports dialog box appears with the exported file.