How can I move a Microsoft Outlook Web Access inbox to an offline inbox? Can I download it using Microsoft Office 2011 for Mac?
2019 update - There now seems to be 2 versions of OWA (outlook.live.com, and outlook.office365.com). These are slightly different but both are now almost functionality-free email and no save message function is provided - best solution is not to use it.
If you have to use it my solution is to set up a parallel gmail account and forward everything to that. Gmail still has a download message option from the Web Interface.