By default, any responses to SMS sent through Outlook Mobile Service (OMS) will come back to your account's default email address. However, it is possible to change which email that responses are sent to on a computer-by-computer basis.
In order to change this, update the "User ID" box under OMS settings to be the username, followed by a vertical pipe, then the desired email address.
For example:
User ID:
username|address@company.com
This address will now receive replies to messages sent through that particular installation of Outlook.