That approach does allow looking up Messages you received, but you'd still need an extra copy of sent Messages and having to find the correct turn and then load it is an unnecessary annoyance.
Or you could use the companion to cut and paste the Messages into the history events.
That way you can see them in-game; who sent them and at what stardate..
(Or use the old history event editor).
Coming not soon is a new and wonderfully improved easier to use tabbed, plug-in Version of the companion!