All SMS messages sent via Mercury SMS will appear in the ‘Activity History’ related list with a Subject of ‘SMS: Sent’ and will record the User that sent the message, the number the message was sent to, as well as the message body.
SMS messages received will show in the ‘Open Activities’ or ‘Activity History’ related list, depending on the Default Task Status setting you applied within the Configuration settings of the Setup & Configuration page. Inbound messages will store a Thread ID which is used to match the inbound message as a reply to an outbound message. 
When reporting on SMS activity, we recommend you create a Report cased on ‘Tasks and Event’s and apply a filter based on the Subject starting with ‘SMS’, viewing Open and Completed Activities.