This could be a number of reasons why an SMS does not get delivered to a mobile.

First of all check inside the contact record history on the status of the SMS text.  If it has been delivered successfully you will see the {DELIVERED} status, as shown in the example above. 

If it says {FAILED} or {QUEUED} then the SMS has not got through because:

1. Problem with the mobile provider of the recipient i.e Orange.Vodafone etc

2. The mobile number is entered incorrectly inside the contact record profile

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