Hi Joeri. SharePoint Online and Outlook integration is very well provisioned; you can achieve most of what you require through the standard out of the box features. You can connect SharePoint Online document libraries, task lists, contact lists and calendars to Outlook very easily. For example, create a new document library in SharePoint Online then from the Actions menu select Connect To Outlook.
The contents of the document library will be transferred to your computer. Outlook will then manage the synchronisation of changes back and forth between your offline copy and SharePoint Online.
If you want to add emails to a SharePoint Online site you can use a neat little trick identified (you can drag and drop emails from Outlook in to a SharePoint Online discussion forum):
http://social.technet.microsoft.com/Forums/en-US/onlineservicesexchange/thread/3506b8b3-32eb-409d-b920-fb8dde45146cI am not sure if it is possible to connect Outlook Web Access to SharePoint Online.
Regards,
Myles
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