When you block someone, they’ll no longer be able to contact you using Messenger. All new messages, calls, and shared conversations are blocked. To block someone, open up Messenger and follow these steps:
Open Messenger on your phone, and press on the friend you wish to block.
Press on the photo of the person on the top.
Then scroll down. Here you’ll find the feature to block or unblock someone.
Important note: Your messages in shared group conversations will still appear for somebody you’ve blocked. Your Facebook.com profile is also still visible. Your Facebook posts, comments, and likes are still visible unless you perform a block on there as well.