Update pairing information so that reconnect doesn't request a PIN.

remoting/webapp/client_screen.js

Index: remoting/webapp/client_screen.js
diff --git a/remoting/webapp/client_screen.js b/remoting/webapp/client_screen.js
index 3698186fd4d0e5ad3a198535f3666d88fd058922..5ca23c144dac1e2b5c7862e2b5a42a2680cc8e2e 100644
--- a/remoting/webapp/client_screen.js
+++ b/remoting/webapp/client_screen.js
@@ -356,6 +356,7 @@ remoting.onConnected = function(clientSession) {
         }
       };
       remoting.HostSettings.save(clientSession.hostId, pairingInfo);
+      remoting.connector.updatePairingInfo(clientId, sharedSecret);
     };
     // Use the platform name as a proxy for the local computer name.
     // TODO(jamiewalch): Use a descriptive name for the local computer, for