How To Block Someone On Facebook Messenger?

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Imagine that someone who is not your friend sends you a message on Facebook messenger or you have been chatting with a friend and the conversation turned sour or went down a road you have no control over and you want to block or bar that person from sending messages and reaching out to you on Facebook messenger.

ON YOUR FACEBOOK APPLICATION:To view your blocked list on your mobile application, there are two ways:
Action 1

• On your Facebook app, tap on the menu button (☰)
• Tap on "Account Settings' (for iPhone users tap on "Settings")
• Tap on "Blocking"

Action 2

• Tap on the menu button (☰)
• Tap on "Privacy shortcuts"
• Scroll down and tap on "How do I stop someone from bothering me?"
• On the drop down menu, tap on "Blocked users"ON YOUR BROWSER:
• Click  in the top right of any Facebook page
• Click "Privacy Shortcuts"
• Click "How do I stop someone from bothering me?"
• Click "View All Blocked Users".

• Source: Learn Facebook Basics

Now, that person can neither send you any messages on Facebook Messenger, nor see your Facebook profile.

Congratulations!
You have now learnt how to block someone on Facebook Messenger app.