By default, yes.
If it’s simply ‘Not Appearing’, than there is a jquery conflict. Check for plugins, and for any jquery inserted into the php file that might be conflicting.
Just realised what it is. I’ve disabled ‘Friends’ in the Component Setup. I didn’t want everyone to have to request frienships just to be able to send mesages. It seems that the drop-down will only show members who are also friends. Not only that, even if you type the members name in the message will not be sent because you are not friends! Seems a little unreasonable since I’ve stated I don’t want friends activated. Can this be overridden?