Hi Christian,
Did you want to save the data in one email account to Exchange Online Outlook Web App? If this is the case, here are my suggestions:
1. Set up your non-Office 365 email account in Outlook and then export the data file to .PST file.
2. Set up your Office 365 email account in Outlook and then import the .PST file to Office 365 account.
Note: For the two steps above, you can refer to this link: http://help.outlook.com/en-us/140/dd401503.aspx
3. The Outlook Data will sync with Outlook Web App.
If I have misunderstood anything, please feel free to let me know.
Thanks,
Eben Liu
