Given a servlet doGet method:

 @Override
    protected void doGet(HttpServletRequest req, HttpServletResponse resp)
            throws ServletException, IOException
    {
        resp.setContentType("text/event-stream");
        AsyncContext ac = req.startAsync(req, resp);
        ServerSentEventsHandler sseHandler = new ServerSentEventsHandler(ac);
        ac.addListener(sseHandler);
    }


In a JSF managed bean, I want to use that ServerSentEventsHandler instance
(that was created in servlet) to write data:

class Task extends TimerTask {
        public void run() {
            try {
                String msg = composeMessage();

                sseHandler.sendMessage(msg, "stock");
            } catch (IOException e) {
            }
        }

    }

Can I use CDI injection here?