Steps for a manual method to backup Office 365 mailbox:
Download & installs MS Outlook on your desktop or laptop.
Go to File >> Add Account & Login into it using the Office 365 user credentials.
The Outlook PST file formed by default after the synchronization of Outlook creates a backup file of Office 365 mailboxes.
Default Location for Outlook file: C:\users\username\Documents\Outlook File
You can use the PST file as a Backup file for safekeeping.
If you want to take backup into PDF file then you have to open emails and Print it as PDF & save it to the desired location on the desktop.