In the client user's settings, ensure that the appropriate permission has been enabled. You'll find that setting under the "General" section:
Toggle the setting for "Messages" to "Enabled" (green), then choose whether they'll be able to simply view message, or if they can create them as well.
Messages are never passed between AgencyAnalytics and your clients. The only communication possible for a client user is between the client user and the agency admin and agency staff users.
Click "save" when finished to apply the new settings.