Hi farringdon,
Do you mean that you used the Office 365 account on Outlook 2002, but now you want to use the Outlook version that Office 365 supported?
If so, you can add the Office 365 account in the Outlook.
Connect Outlook to This Account: http://help.outlook.com/en-us/140/ms.exch.ecp.useoutlookanywhere.aspx
If you just want to import the data to Outlook that Office 365 supported, you can refer to the following link to import the data to Outlook: http://help.outlook.com/en-us/140/dd401503.aspx
Currently, Office 365 supports the use of Microsoft Office Outlook 2007 or later versions.
Thanks,
Anna Shi