To take Backup of Office 365 Emails without an issue, there are several third-party software provided in the online marketplace. This Office 365 Email backup process is tough to perform so these tools make it effortless. All available software claims that they are best it ups to users which will easy to use for them.
You can also check a free demo version of the Shoviv Office 365 Backup and Restore Tool. It is a complete solution to perform the office 365 backup process. This software is highly performing and capable to restore data from OST/PST files to Office 365 mailboxes. After completing the process of backup it provides a report for future reference.
Additionally, this software can run without Outlook independently without any difficulty.
Source for more: Office 365 Backup