Within each record, there's a check box with Opt Out SMS functionality. By default, this is unchecked, however if the recipient of a text message replies with ‘stop’ to a message that has been sent out, this check box will automatically be ticked, and messaging from this record will be disabled.
When the Opt-Out SMS box is checked, the Conversations button will no longer be shown:
As this record has opted out it will not appear on Group SMS Saved lists if it was part of one prior to Stop Sending being enabled.
Note - If the number is attached to different records it will still be able to receive SMS, so you will need to update these records where applicable. Also, SMS replies are saved in the latest record of the “MessageMedia SMS Receipt” custom record.