Set up your MailService account in Outlook.com (Hotmail)
Click on the gear icon and choose 'Options'.
Go to 'Aliases: manage or choose a primary'.
Click 'Add email'.
Choose 'Add an existing email address as a Microsoft account alias' and enter you MailService address.
After adding the alias you have to verify it.
To send the verification email click on 'Send email'. You will receive a verification email from Microsoft, in which you have to click on the verification link.
Now your alias is verified so you can make it a primary alias.
Just click 'Yes' to make the address your primary alias.
Your alias is set, now you can send emails from your MailService address by choosing it from the drop-down menu where the sending address is shown when composing an email.