Note: The instructions on SMS gateway configuration is available here.
Check if the SMS gateway works properly.
Check if sms.notSent event is generated on the customer’s activity list. If so, check the event parameters to see the source of the issue. It may also be caused by time limits imposed by the SMS provider.
Check if sms.capping event is generated on the customer’s activity list. If so, the message wasn’t sent due to the limit of SMSes that can be sent to a customer in a defined time frame.