Hi @ShineVv0823 ,
The reason why the Sms SRs are not synced with the broadLogs is usually the Regex of the SR is not correctly declared as per the PDU sent by your SMS provider.
So, go to your SMS external account > Mobile>SMS specificities and check the Regex declared for the SR and with the PDU that you received. If you want you can also reach out to your Sms provider to get the Regex for the SR extraction.
Also, the following is the document you can refer to troubleshoot more for the SR sync issue: here
Br,
Shubham