To access a log of all messages sent you to need to head over to Responder or Bulk and select SMS logs. 

Accessing the logs will allow you to search for messages using:

• Time and Date
• Campaign
• Responder
• Push
• Lead ID | Phone number | Email address
• Success | Failed delivery

Below you can see an example of an SMS message that was sent. The example gives you a breakdown of information linked to the given send such as message body, URL, time sent and more. 

The above information can be useful when dealing with customer or internal queries.