Question 

Why can't users with a particular role see any forms on the Messaging tab or when they click the Send Messages widget, but they can see View Sent Messages?

Answer

In addition to having a role with the 'Send Messages' function, a user or role needs to have sender permissions for a form to see it on the Messaging tab or when they click the Send Messages widget.

To grant a user or role form sender permissions:

1. Click on the Workflows tab.
2. In the list of workflows, click the name of your workflow.
3. For the form you want to edit sender permissions for, click the deployment drop-down menu (to the left of the Edit menu) and select Sender Permissions.
4. In the search field, type the name of the role or a user and select it when it appears.
5. Once it is added to the list, click Save Changes.