Ruthie, I'm not 100% sure I fully understand your question. So I apologize if I'm totally off track here.
To see a list of messages sent by any particular member, you can go under "Admin->Members" and click on the member's name. Then at the top, click under "Activity History"; under "Actions" choose "Sent message" in the scroll down menu and click the Search button. You will then see a list of all their sent messages which, I assume, would include messages requiring approval.