回复：Should I tell my manager? - Yes. I would if I were you.

However, I would tell her in a little bit twisted way that I saw the opporunity and just "asked" around and then ask her if there is any chance for me to have the internal transfer because it appears not much for me to do right now.

I have to say that it might hurt her by saying "not having enough to do" to your director but the done is done. You have to wait and see.

Internal transfer somehow is trickier than that it looks.