To back up all public Exchange Online folders, you must add the public folders to an Exchange Online app.
From the navigation pane, go to Protect > Applications > Office 365.
The Office 365 apps page appears.
In the Name column, click the Exchange Online app to add the public folders to.
The app page appears.
On the Content tab, in the All public folders row, click the action button , and then select Manage > Change plan.
The Edit association dialog box appears.
Select the Office 365 plan to use for the public folders, and then click Save.
To back up the public folders immediately, do the following:
In the All public folders row, click the action button , and then select Back up.
A message prompts you to confirm submission of the job.
After the backup completes, to view the backed-up public folders, on the Office 365 app page, in the row for the app, click the action button , and then click Restore.