ExternalContext#redirect is not add the windowId to url params.

action="/AnotherView.xhtml"

String requestContextPath = facesContext.getExternalContext().getRequestContextPath();
facesContext.getExternalContext().redirect(requestContextPath + "/myTarget");

@WebServlet(name = "MyServlet", urlPatterns = { "/myTarget" })
public class MyServlet extends HttpServlet {

  @Override
  public void doGet(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {
    final String windowId = request.getParameter(ConversationConsts.WINDOW_ID_PARAM); // null
    // 
}

public void redirect(String url) throws IOException
{
  FacesContext facesContext = getCurrentFacesContext();
  PartialViewContext partialViewContext = facesContext.getPartialViewContext(); 
  if (partialViewContext.isPartialRequest())
  {
    PartialResponseWriter writer = partialViewContext.getPartialResponseWriter();
    this.setResponseContentType("text/xml");
    this.setResponseCharacterEncoding("UTF-8");
    this.addResponseHeader("Cache-control", "no-cache");
    writer.startDocument();
    writer.redirect(url);
    writer.endDocument();
    facesContext.responseComplete();
  }
  else if (_servletResponse instanceof HttpServletResponse)
  {
    ExternalContext externalContext = facesContext.getExternalContext();
    Map<String, String> requestParameterMap = externalContext.getRequestParameterMap();
    String windowId = requestParameterMap.get(ResponseStateManager.CLIENT_WINDOW_URL_PARAM);
    if (windowId != null)
    {
      url = addWindowIdIfNecessary(url, windowId);
    }
    ((HttpServletResponse) _servletResponse).sendRedirect(url);
    facesContext.responseComplete();
  }
  else
  {
    throw new IllegalArgumentException("Only HttpServletResponse supported");
  }
}

private String addWindowIdIfNecessary(String url, String windowId)
{
  if(url.contains(ResponseStateManager.CLIENT_WINDOW_URL_PARAM + "="))
  {
    return url;
  }
      
  StringBuilder newUrl = new StringBuilder(url);
  if(url.contains("?"))
  {
    newUrl.append("&");
  }
  else
  {
    newUrl.append("?");
  }
  newUrl.append(ResponseStateManager.CLIENT_WINDOW_URL_PARAM);
  newUrl.append("=");
  newUrl.append(windowId);
  return newUrl.toString();
}

<factory> 
  <lifecycle-factory>org.primefaces.clientwindow.PrimeClientWindowLifecycleFactory</lifecycle-factory>
</factory>

<context-param>
  <param-name>javax.faces.CLIENT_WINDOW_MODE</param-name>
  <param-value>url</param-value>
</context-param>