Hello!
Tested this connection. As you said, everything works through the browser, the device on the local network sends SMS on HTTP POST / GET request.
Also, requests go through and SMS is sent through many other applications (for example, Advanced REST Client), however, problems arise with the docklight scripting application. Have you tested this application with other devices / routers (not Teltonika)?
Did everything work correctly?
BR
Aliaksandr