I posted a previous postServlet 3.0 Tip: How Do I Get to Another Servlet Context? which demonstrates how to get to another context. This extends that discussion by showing how to forward a JSF request to the other context and have the servlet output the results.
Here is the basic code to be called from the JSF page.
Here is the method.
Here is the servlet I called.
Note: If you were going to pass it to JSF, you would need to remove the view state since the Faces Servlet receiving the values would result in a ViewExpiredException since this view state is not in the target Faces Servlet.