Outlook 2013 hotmail_**********@live.com sending on behalf of ********@******.com

I am trying to reorganize my emailing and ran into a couple of issues here...

I have several business and private email accounts. Up until now I used POP to download them to Outlook 2013. I decided to make use of EAS features, so have one EAS account handling all email accounts, calendar, etc.

I can add respective smtp servers to the respective accounts, so now I can send emails from outlook.com with the correct sender in the header. However I mostly use Outlook 2013. Syncronization of emails (also sent items, spam, etc.), calendar, tasks works fine. But when sending an email from Outlook 2013 I can choose the sender (I have only one account, the EAS account set in Outlook) account and the sender email, but the recipient sees in the header this hotmail_**********@live.com sending on behalf of ********@******.com thing. Any solutions to this?

Rgds,

Zoltan