I've got a Microsoft Live account that is tied to my Gmail address (firstname.lastname@example.org). Since sharing documents with people sends emails from email@example.com, their replies go to my outlook.com inbox, which I don't check.
I tried to set up forwarding (Options > Email Forwarding) and when I put in firstname.lastname@example.org, I got the error 'You can't forward mail to your original address or any of your aliases.'
Which wasn't going to work for me.
So I found a quick hack that worked -- simply change the forwarding address to email@example.com, or firstname.lastname@example.org. With Gmail, it will allow you to use + signs and extra dots to help filter your mail. That's it!