Approve a SharePoint workflow task using SharePoint Web Services / Object Model

Question

I have created a workflow is SharePoint Designer and associated it with a list. The workflow creates an approval process, so SharePoint creates a task in the Tasks list so t

Answer 1

After a lot of trials and investigation I just had the following code working to approve the task

SPSite site = new SPSite("http://servername/");
using (SPWeb web = site.OpenWeb())
{
    SPList list = web.Lists["TestList"];
    SPListItem item = list.GetItemById(22);
    SPWorkflow workflow = item.Workflows[0];
    SPWorkflowTask task = workflow.Tasks[0];

    Hashtable ht = new Hashtable();             
    ht[SPBuiltInFieldId.Completed] = "TRUE";
    ht["Completed"] = "TRUE";
    ht[SPBuiltInFieldId.PercentComplete] = 1.0f;
    ht["PercentComplete"] = 1.0f;
    ht["Status"] = "Completed";
    ht[SPBuiltInFieldId.TaskStatus] = SPResource.GetString(new CultureInfo((int)task.Web.Language, false), Strings.WorkflowStatusCompleted, new object[0]);
    ht[SPBuiltInFieldId.WorkflowOutcome] = "Approved";
    ht["TaskStatus"] = "Approved";
    ht["FormData"] = SPWorkflowStatus.Completed;

    web.AllowUnsafeUpdates = true;
    SPWorkflowTask.AlterTask((task as SPListItem), ht, true);
}

I suspect that ht["TaskStatus"] = "Approved"; is that attribute that solved it. Anyway I will try to narrow on the set of properties that need to be changed.