How to assign a user in Conversation to an existing contact

Thanks @qlambert That did it. Although, it would be nice to add search option in the panel to avoid having to find an email or phone number associated to a contact. In my first example, I had to go to search for the company, then click the assigned contact, copy and paste the email. Little cumbersome.

Btw- do you have a better place to submit suggestion. See my comment in Product Suggestions and Improvements - #9 par monocat

Also another suggestion that I had posted: CRM Suggestion: Add ability to assign contacts to companies with no email