does control come back to the webapp which forwarded request to another webapp?

I have 2 web apps.

1. A.war
2. B.war

both have been deployed in same app server. A request comes to A.war and it forwards the request to B.war via

context.getServletContext("appname of B").getRequestDispatcher("uri").forward(request, response);

once the request is forwarded from A to B and then once the processing is completed on B, does the control come back to web app A or web app B directly sends the request to the client (browser)?

In other words , is it a separate Thread that would be executed in web app B in this case and it sends the response directly to the user?