<aura:component controller="ContactController" access="global">
<aura:attribute name="taskInstance" type="Task" default="{ 'sobjectType':'Task' }"/></aura:component>

doSave : function(component, event) {
    var action = component.get("c.saveUpdatedTaskInfo");
    var t = component.get("v.taskInstance");
    action.setParams({ "taskInst": t});
}

@AuraEnabled
public static Task saveUpdatedTaskInfo(Task taskInst) {

    if(taskInst.Org_Identifier__c=='Org 1')
    {
        update taskInst;
    }
   else
    {
        Task_Trigger_Handler.processTasks(new List<Task>{taskInst});
    }

    return taskInst;
}

public class Task_Trigger_Handler
{
    public static void processTasks(List<Task> tskLst)
    {
        for(Task tsk:tskLst)
        {
            if(tsk.Org_Identifier__c=='Org 1')
            {
                //invoke the callout method
                invokeTaskCallout(tsk.id,tsk.Subject,.........);
            }
        }
    }



@future(callout=true)
public static void invokeTaskCallout(String id,String .......)
{
    //fetch from custom settings
    CustomSettings__c customSettings=[SELECT password__c,rest_endpoint__c,token_endpoint__c,username__c
                                                FROM customSettings__c LIMIT 1];

    //establish connection and fetch the session id
    String endpoint1= customSettings.token_endpoint__c;
    Httprequest req = new HttpRequest();
    req.setMethod('POST');
    req.setHeader('Content-Type','application/x-www-form-urlencoded');

    req.setBody('grant_type=password' +
          '&client_id=' + customSettings.Consumer_key__c+
          '&client_secret=' + customSettings.Consumer_Secret__c+
          '&username=' + customSettings.username__c+
          '&password=' + customSettings.password__c
       );
    req.setEndpoint(endpoint1);
    Http http = new Http();
    HttpResponse res;
    String Access_Token;
    try
    {
        res = http.send(req);
        system.debug('body1:'+res.getBody());
        JSONParser parser = JSON.createParser(res.getBody());
        while (parser.nextToken() != null)
        {
            if ((parser.getCurrentToken() == JSONToken.FIELD_NAME) && (parser.getText() == 'access_token'))
            {
                parser.nextToken();
                Access_Token = parser.getText();
            }
        }
    }
    catch(system.CalloutException e)
    {
        system.debug('error'+e);
    }

    system.debug('access token'+Access_Token);

    String endpoint2=customSettings.rest_endpoint__c;
    HttpRequest req1 = new HttpRequest();
    HttpResponse res1 = new HttpResponse();
    Http http1 = new Http();
    String str='{"id":"'+id+'","Subject":"'+Subject+'","ActivityDate":"'+String.valueOf(ActivityDate)+'","Category":"'+Category+'","Description":"+Description+","Status":"'+Status+'","Internal_Deadline":"'+String.valueOf(Internal_Deadline)+'","Actual_Deadline":"'+String.valueOf(Actual_Deadline)+'"}';
    req1.setEndpoint(endpoint2);
    req1.setMethod('PUT');
    req1.setHeader('content-type', 'application/json');
    req1.setHeader('Accept', 'application/json');
    req1.setHeader('Authorization', 'OAuth '+Access_Token);
    req1.setBody(str);
    req1.setCompressed(true); // otherwise we hit a limit of 32000

    try
    {
        res1 = http1.send(req1);
    }
    catch(System.CalloutException e)
    {
        System.debug(res1.toString());
    }

}