sync: move internal_api components used by chrome/browser into internal_api/public

sync/internal_api/js_mutation_event_observer.h

Index: sync/internal_api/js_mutation_event_observer.h
diff --git a/sync/internal_api/js_mutation_event_observer.h b/sync/internal_api/js_mutation_event_observer.h
index 60a33a268523314c8e9a86c3aff0f380e30d77eb..33573ff41b6bed5ce07a4d516976f2a536073999 100644
--- a/sync/internal_api/js_mutation_event_observer.h
+++ b/sync/internal_api/js_mutation_event_observer.h
@@ -12,9 +12,9 @@
 #include "base/compiler_specific.h"
 #include "base/memory/weak_ptr.h"
 #include "base/threading/non_thread_safe.h"
-#include "sync/internal_api/sync_manager.h"
+#include "sync/internal_api/public/sync_manager.h"
+#include "sync/internal_api/public/util/weak_handle.h"
 #include "sync/syncable/transaction_observer.h"
-#include "sync/util/weak_handle.h"
 
 namespace tracked_objects {
 class Location;