You have noticed that Facebook notifies for the messages from your Facebook friends in Inbox, but there is also a separate Inbox for messages from people who are not your Facebook friends but still can send you messages. In following you can find that how to access hidden Inbox in Facebook.
Facebook Other Messages Inbox
Step-1
Login to your Facebook, and click on Messages link in left panel
Step-2
Click on “Other” to view messages from Facebook users who are not your friends right now
yes there is Other Inbox in Facebook.
Before I was not aware about Other inbox of Facebook, thanks.
Other facebook inbox is really useful, its first time to get familiar to this feature of Facebook.