When trying to save/send a "tracked" Outlook Email in Microsoft Dynamics CRM for Microsoft Office Outlook, you may encounter this Offline Error message: "The sender does not have an e-mail address in Microsoft Dynamics CRM. Do you want to send the e-mail? If you click Yes, the e-mail will be sent out, but no corresponding activity will be created in Microsoft Dynamics CRM". This applies for both Microsoft CRM 4.0 On-Premise and CRM Online.
Pretty obvious – this is caused by the Microsoft CRM User’s "Primary E-mail" field not having a value. Updating this field with a valid email will resolve the issue.