App windows with ids should remember fullscreen state.

chrome/browser/ui/cocoa/apps/native_app_window_cocoa.mm

 // 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 "chrome/browser/ui/cocoa/apps/native_app_window_cocoa.h"
 
 #include "apps/app_shim/extension_app_shim_handler_mac.h"
 #include "base/command_line.h"
 #include "base/mac/mac_util.h"
 #include "base/strings/sys_string_conversions.h"
@@ skipping 450 matching lines @@
   NSScreen* screen = [[NSScreen screens] objectAtIndex:0];
   NSRect frame = restored_bounds_;
   gfx::Rect bounds(frame.origin.x, 0, NSWidth(frame), NSHeight(frame));
   bounds.set_y(NSHeight([screen frame]) - NSMaxY(frame));
   return bounds;
 }
 
 ui::WindowShowState NativeAppWindowCocoa::GetRestoredState() const {
   if (IsMaximized())
     return ui::SHOW_STATE_MAXIMIZED;
+  if (IsFullscreen())
+    return ui::SHOW_STATE_FULLSCREEN;
   return ui::SHOW_STATE_NORMAL;
 }
 
 gfx::Rect NativeAppWindowCocoa::GetBounds() const {
   // Flip coordinates based on the primary screen.
   NSScreen* screen = [[NSScreen screens] objectAtIndex:0];
   NSRect frame = [window() frame];
   gfx::Rect bounds(frame.origin.x, 0, NSWidth(frame), NSHeight(frame));
   bounds.set_y(NSHeight([screen frame]) - NSMaxY(frame));
   return bounds;
@@ skipping 438 matching lines @@
 ShellNSWindow* NativeAppWindowCocoa::window() const {
   NSWindow* window = [window_controller_ window];
   CHECK(!window || [window isKindOfClass:[ShellNSWindow class]]);
   return static_cast<ShellNSWindow*>(window);
 }
 
 void NativeAppWindowCocoa::UpdateRestoredBounds() {
   if (IsRestored(*this))
     restored_bounds_ = [window() frame];
 }