Display post response after submission using hook.

Something like:

class MyPlugin {
	public function MyPlugin() {
		// note that you'll want to hook to the right service; this hooks to all
		add_filter('Forms3rdPartyIntegration_service', array(&$this, 'adjust_response'), 10, 2);
	}

	public function adjust_response($body, $refs) {
		// use 'attach' to inject to regular email
		// use 'message' to inject to page
		$refs['attach'] = 'custom message in email';
		$refs['message'] = 'custom message on page';
	}
}

new MyPlugin(); // engage!