I have:
Outlook.com account with 1 alias (I didn't come from hotmail) 
Apple Mail desktop client.
iPhone
 
In the past my desktop mail client allowed me to check mail individually from different addresses from gmail, yahoo, etc. and reply from that same address via a drop down menu.  I'm guessing because of the structure of an alias vs. linked accounts though this has not been the case for outlook.com.

When I select to send from my alias address in the desktop mail client it sends and shows that it sends from the alias address.  But when I go to outlook.com and check it actually never sends from my alias address as it should, but it sends from my primary address.  It's really confusing for customer service people who have multiple cases open for me because of the different email addresses showing up.

Would someone be able to provide a workaround for this?  Right now the alias setup vs. the linked account setup is becoming more of a pain to work with my desktop client and my phone.

Thanks a ton for your help!