Hi Suzanne,
It's better to connect the Time Warner accounts to Outlook.com -
Outlook.com - Connected Accounts Settings Page
By connecting the accounts you'll be able to have Outlook.com download all emails received by the Time Warner directly from their servers.
This solution is better than forwarding the email to Outlook.com because the forwarded emails have the potential to appear to be sending/relaying from unapproved sources (according to the sender policies) and the outlook.com anti-spam systems.
Don't forget to turn off the forwarding after you have the accounts connected.