First, check the customer account page > "Engagement" tab. Did the SMS send, and if so, is there an error message? If not, ensure that the customer has a valid phone number and has not opted out of SMS.
Next, check your communication preferences > "Ready SMS". If it is set to none, this SMS will not send. If set to "managed" or "not-managed" it will only go to customers with those settings.
Finally, ensure that the order was a store order and the the customer is able to receive SMS.
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