It looks like a duplicate of old issue https://github.com/localstack/localstack/issues/78
But now it's reproducible for me with the latest version of LocalStack. 
aws_stack.create_sqs_queue(self.TEST_SQS_QUEUE)
        
        result = connect_api_gateway_to_sqs('test_gateway4', stage_name=self.TEST_STAGE_NAME,
            queue_arn=self.TEST_SQS_QUEUE, path=self.API_PATH_DATA_INBOUND)
        
        test_data = {'spam': 'eggs'}
        url = INBOUND_GATEWAY_URL_PATTERN.format(
            api_id=result['id'],
            stage_name=self.TEST_STAGE_NAME,
            path=self.API_PATH_DATA_INBOUND
        )
        result = requests.post(url, data=json.dumps(test_data))
        self.assertEqual(result.status_code, 200)
        messages = aws_stack.sqs_receive_message(self.TEST_SQS_QUEUE)['Messages']
        self.assertEqual(len(messages), 1)
        self.assertEqual(json.loads(base64.b64decode(messages[0]['Body'])), test_data)
    def test_api_gateway_http_integration(self):
        test_port = 12123
        backend_url = 'http://localhost:%s%s' % (test_port, self.API_PATH_HTTP_BACKEND)
        
        class TestListener(ProxyListener):