There are several User Permissions that control the ability to send text messages.
Go to Tools > Manage Users & Permissions > User IDs (click on a UserID) > User Permissions (left) to set the permissions.
Note: If a User is logged in when changes are made to their permissions, they'll have to log out and then back in before the changes will take effect.
These are the permissions related to Text Messaging:
|Text Messages Settings
|Send Text Messages
|Email Families & Email Student Schedules
See Permissions for Jackrabbit Users for more information.