Another third party tool that I can suggest you is Office 365 Backup Software that allows to save backup of Office 365 mailboxes to multiple file formats - PST, PDF, EML, EMLX, MBOX and MSG. This tool provides complete and accurate solution for exporting Outlook OWA webmail to On-premises, without any problems.

To get complete software working, your can also download its FREE demo edition that supports to export first 100 emails and 25 other items to desktop.