It is a little more complicated. I found to see my sent messages I had to go into my Personal Messages (under the My Messages tab on the top bar) and then go into my Settings and select the option:
Save a copy of each personal message in my sent items by default.
Once I did that, I could access a copy of any message or reply to a message that I had sent. Before I changed the settings, it defaulted to not save my sent messages.
Naomi