Depending on the 3rd party service options the most standard way would be to call the rest service on the third party app and perfrom a POST to send the data. Other options would be to use webservices, if the 3rd party app has a SOAP service available. If these services are not available you might consider the database connector module to send the data to the 3rd party database directly.
Without knowing anything about the 3rd party app it is difficult to provide a definitive answer, but you seem to be on the right track.