Methods defined as TestMethod do not support Web service callouts 
Stack Trace: null

@isTest
  private class testUpdateContactAfterConverted {
    static testMethod void myUnitTest() {
    	
 // This causes a fake response to be generated
        Test.setMock(WebServiceMock.class, new WebServiceMockImpl());
        
        // Call the method that invokes a callout
        String output = WebSvcCallout.callEchoString('Hello World!');
        
        // Verify that a fake result is returned
        System.assertEquals('Mock response', output);    	

	Test.StartTest();
    	
    // Create new test lead
    Lead myLead = new Lead(LastName = 'Fry', Company='Fry And Sons', LeadSource = 'Advertising', Lead_Source_Detail__c = 'PPC');
    insert myLead;

    // Convert test lead
    Database.LeadConvert lc = new Database.LeadConvert();
    lc.setLeadId(myLead.id);
    
    // Check conversion
    LeadStatus convertStatus = [SELECT Id, MasterLabel FROM LeadStatus WHERE IsConverted=true LIMIT 1];
    lc.setConvertedStatus(convertStatus.MasterLabel);
    
    // Declare successful
	Database.LeadConvertResult lcr = Database.convertLead(lc);
	System.assert(lcr.isSuccess());
	if(lcr.isSuccess())
	{
	Contact newContact = [Select Id from Contact LIMIT 1];
	updateContactAfterConvertedFuture.myMethod(newContact.id);
	}
	Test.StopTest();    

    }
  }

@isTest
global class WebServiceMockImpl implements WebServiceMock {
   global void doInvoke(
           Object stub,
           Object request,
           Map<String, Object> response,
           String endpoint,
           String soapAction,
           String requestName,
           String responseNS,
           String responseName,
           String responseType) {
       docSample.EchoStringResponse_element respElement = 
           new docSample.EchoStringResponse_element();
       respElement.EchoStringResult = 'Mock response';
       response.put('response_x', respElement); 
   }
}

public class WebSvcCallout {
    public static String callEchoString(String input) {
        docSample.DocSamplePort sample = new docSample.DocSamplePort();
        sample.endpoint_x = 'http://api.salesforce.com/foo/bar';
        
        // This invokes the EchoString method in the generated class
        String echo = sample.EchoString(input);
        
        return echo;
    }   
}

public class docSample {
    public class EchoStringResponse_element {
        public String EchoStringResult;
        private String[] EchoStringResult_type_info = new String[]{
                            'EchoStringResult',
                            'http://doc.sample.com/docSample',
                             null,'0','1','false'};
        private String[] apex_schema_type_info = new String[]{
                             'http://doc.sample.com/docSample',
                             'true','false'};
        private String[] field_order_type_info = new String[]{
                             'EchoStringResult'};
    }
    public class EchoString_element {
        public String input;
        private String[] input_type_info = new String[]{
                              'input',
                              'http://doc.sample.com/docSample',
                               null,'0','1','false'};
        private String[] apex_schema_type_info = new String[]{
                               'http://doc.sample.com/docSample',
                               'true','false'};
        private String[] field_order_type_info = new String[]{'input'};
    }
    public class DocSamplePort {
        public String endpoint_x = 'http://YourServer/YourService';
        public Map<String,String> inputHttpHeaders_x;
        public Map<String,String> outputHttpHeaders_x;
        public String clientCertName_x;
        public String clientCert_x;
        public String clientCertPasswd_x;
        public Integer timeout_x;
        private String[] ns_map_type_info = new String[]{
                          'http://doc.sample.com/docSample', 'docSample'};
        public String EchoString(String input) {
            docSample.EchoString_element request_x = new 
                                           docSample.EchoString_element();
            request_x.input = input;
            docSample.EchoStringResponse_element response_x;
            Map<String, docSample.EchoStringResponse_element> response_map_x = 
                       new Map<String, docSample.EchoStringResponse_element>();
            response_map_x.put('response_x', response_x);
            WebServiceCallout.invoke(
              this,
              request_x,
              response_map_x,
              new String[]{endpoint_x,
              'urn:dotnet.callouttest.soap.sforce.com/EchoString',
              'http://doc.sample.com/docSample',
              'EchoString',
              'http://doc.sample.com/docSample',
              'EchoStringResponse',
              'docSample.EchoStringResponse_element'}
            );
            response_x = response_map_x.get('response_x');
            return response_x.EchoStringResult;
        }
    }
}