Few points what I know are as following:
- MME and MSC interface i.e. SGs should active for SMS service
- UE triggers "Service Request" if it is in Idle Mode (optional)
- UE sends "SMS within the NAS container. S1-AP Uplink NAS Transport message carries the NAS message till MME.
- MME prepares and sends the SMS (within the NAS container) to MSC by using the SGsAP-UPLINK-UNITDATA message.