You can do what @Emmanuel suggested or you can pass the BasicHttpContext between the HttpClients you are creating.
Example Use of context and cookies, complete code here
HttpClient httpclient = new DefaultHttpClient();
// Create a local instance of cookie store
CookieStore cookieStore = new BasicCookieStore();
// Create local HTTP context
HttpContext localContext = new BasicHttpContext();
// Bind custom cookie store to the local context
localContext.setAttribute(ClientContext.COOKIE_STORE, cookieStore);
HttpGet httpget = new HttpGet("http://www.google.com/", localContext);