Thank you for the update.
We cant assign tasks from an Exchange account to a Hotmail account.
But, if we want to assign tasks from an Exchange server account to another one which use a different Exchange server, we need to run the PowerShell described in the article I mentioned before to enable the TNEF.
If you want to assign tasks from O365 .edu to another O365 .edu, I believe this can be done. But for your situation, you want to assign tasks from an Office 365 .edu account to an external Exchange account, Im not sure if this is possible. The
remote domains setting is controlled by Exchange Hub, Hub can do this within the organization but not sure if its out of the organization.
Since we are not the best resource for Office 365, you can post your question in Office 365 forum to get further assistance:
http://community.office365.com/en-us/forums/default.aspx
The reason why we recommend posting appropriately is you will get the most qualified pool of respondents,
and other partners who read the forums regularly can either share their knowledge or learn from your interaction with us.
Thank you for your understanding.
Regards,
Steve Fan
Forum Support