Did you type your password of FB? This looks like a phishing scam, but it may be just a stupid app grow hacking. Are you sure that the app that wanted to be installed is the real FB-messenger app?
I was already logged in to FB and android/chrome remembered it. I didn't have to type password. Yes, its the real messenger app. I was wondering what is the point of sending review account email in this i.e.after sending the mail about a message and when the user chosen to interact and follow that email to message flow. Maybe its not much.