A Salesforce user belonging to the Customer Portal Super user Profile or registered under the Customer Portal Manager Custom user License doesn't allow Modify All permission to any object in Salesforce. They represent a User or Group that is a member of a public group. 


As a result, if this user profile is responsible for an auto trigger of an SMS, the SMS won't go. To be able to send an SMS through the SMS Magic app, a user profile needs to have "Modify All" access to all the objects belonging to the SMS Magic application. Being a Customer Portal Super user restricts the access and hence the request fails.

Reference: https://developer.salesforce.com/docs/atlas.en-us.api.meta/api/sforce_api_objects_groupmember.htm