This wikiHow article shows you how to unblock someone you previously blocked on Facebook Messenger so they can contact you again.
Steps
Method 1 of 3: iPhone and iPad

Step #1. Open the Messenger app
This is the app with a lightning bolt in a blue speech cloud.

Step #2. Tap on your profile icon
It's the blue person-shaped icon in the top left corner of the screen.

Step #3. Tap on People
You will find this under the option Notifications.

Step #4. Tap on Blocked
You should be able to find this at the very bottom.

Step 5. Tap the name of the person you want to unblock

Step 6. Move the slider next to "Block chat messages" to disable the option
He will turn white. Now you can contact this person and he or she with you.
Method 2 of 3: Android

Step #1. Open the Messenger app
This is the blue app in the form of a speech cloud with a lightning bolt in it.

Step #2. Tap on your profile icon
It's the gray person-shaped icon in the top right corner of the screen.

Step #3. Scroll down and tap on People
You will find this under the option Text message.

Step #4. Tap on Blocked People
This is the last option.

Step 5. Tap on Unblock next to the person's name

Step 6. Tap on Unblock in Messenger
This is the first option. You can now message each other again with Facebook Messenger.
Method 3 of 3: Computer

Step 1. Go to www.facebook.com with your browser
Log in to your Facebook account if necessary

Step 2. Click on ↓
You'll find this in the top right corner of the screen.

Step 3. Choose Settings
This option can be found in the lower half of the menu.

Step #4. Click on Blocked
This is one of the menu options on the left side of the page. This option can be found in the top half of the list.

Step 5. Scroll down to the "Block Chat Messages" section
The names you'll find under this heading are all people you've blocked and who can't message you in Messenger.

Step 6. Click Unblock next to the person's name
Make sure the name is to the right of Block chat messages from. You can now message each other again with Facebook Messenger.