1. Log in as a user (user 1). Check that user 1's messaging settings are set so that "Personal messages between users" go to email while not online and to a popup window while online.
2. Log user 1 out.
3. Wait 5 minutes so that user 1 is considered to be offline (assuming the default setting in Settings > Site administration > Plugins > Blocks > Online users).
4. Log in as another user (user 2).
5. Send a message from user 2 to user 1.
6. Verify that user 1 receives an email notification of the message.