java swing thread callback

I'm trying to write some client/server application using swing. I have a problem with threads communication. I can't understand how to send some data from EDT back to running thread.

class SwingUI extends JFrame implements IUpdater{

    @Override
    public void askPermission(String str) {
        int i = JOptionPane.showConfirmDialog(this, str);
        //  (?)Send i back
    }

}

class Connection implements Runnable{

    IUpdater updater;

    Connection(IUpdater u){updater = u;}

    @Override
    public void run() {
        String command = "download_file"; //=getCommand(); from a socket
        if(command.equals("download_file")){

            SwingUtilities.invokeLater(new Runnable() {

                @Override
                public void run() {
                    updater.askPermition(command);
                }
            });
            //  (?)wait until user answers
            //  int answ = getAnswer();
            //  if answ == OK
            System.out.println("Sending_File");
            //  if answ == DENY
            //System.out.println("Denied");
        }
    }

}



interface IUpdater{
    void askPermission(String str);
}

I need to get somehow response from userUI. Maybe not just int value but List object.

E.g after connection I need to prepare some data for certain client in userForm and then send it. What should I do?

Swingworker allows only to publish data to EDT or fire events which EDT's listening, not to receive messages.

Also I have to make running thread wait somehow. I'm not sure that sleep(n) until some variable changes is a good idea but I do not know how to use monitors in this case and should I. Maybe there are some design patterns solving it?

I'm sure that it is a common situation but I couldn't find any information about it.