This guide will show you how to check messages from people who are not your friends on Facebook.
Steps

Open the Messenger app. The app icon is a chat bubble with a white lightning bolt inside, which can be found on your home screen or in your app tray.

Log in to Messenger. If you're not logged in, enter your phone number and tap Continue, then input your password.

Tap on the Address Book icon. This icon consists of three horizontal lines, each preceded by a dot, located in the bottom-right corner of the screen.

Select Message Requests (Pending messages). This option is located next to the green chat bubble icon with three white dots inside. By selecting this, you can view messages received from people who aren't your Facebook friends.