[DevTools] Move DispatchOnDevToolsFrontend to embedder.

content/shell/browser/shell_devtools_frontend.cc

 // Copyright 2013 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #include "content/shell/browser/shell_devtools_frontend.h"
 
 #include "base/command_line.h"
 #include "base/path_service.h"
 #include "base/strings/stringprintf.h"
 #include "base/strings/utf_string_conversions.h"
@@ skipping 125 matching lines @@
 }
 
 void ShellDevToolsFrontend::HandleMessageFromDevToolsFrontendToBackend(
     const std::string& message) {
   DevToolsManager::GetInstance()->DispatchOnInspectorBackend(
       this, message);
 }
 
 void ShellDevToolsFrontend::DispatchOnInspectorFrontend(
     const std::string& message) {
-  if (frontend_host_)
-    frontend_host_->DispatchOnDevToolsFrontend(message);
+  std::string code = "InspectorFrontendAPI.dispatchMessage(" + message + ");";
+  base::string16 javascript = base::UTF8ToUTF16(code);
+  web_contents()->GetMainFrame()->ExecuteJavaScript(javascript);
 }
 
 void ShellDevToolsFrontend::InspectedContentsClosing() {
   frontend_shell_->Close();
 }
 
 }  // namespace content