So you can send the SMS by going to the link http://192.168.1.1/cgi-bin/sms_send?username=user1&password=user&number=003700000000&text=testmessage and you receive the message, however, when you try to do that from the SMS, the SMS is not sent?
If the PLC uses CLI commands, it should look like this: curl -X GET "http://192.168.1.1/cgi-bin/sms_send?username=user1&password=user_pass&number=0037000000000&text=testmessage"
If the browser link works, and the sending on the PLC does not work, I would double-check on how to set it up on the PLC and if all the settings are correct, IP, number, user, pass.