This wikiHow teaches you how to delete archived posts on Facebook.
Steps

Step 1. Go to Facebook
The Facebook Messenger app does not allow you to view your archived messages. So you really need a computer to do this.
If you're not already logged in to Facebook, enter your email address and password and click 'Login'

Step 2. Click on the 'Messages' tab
You'll find this in the top right corner of the Facebook toolbar between the 'Friend Requests' and 'Notifications' tabs. The messages tab has an icon of two overlapping speech bubbles.

Step 3. Click on 'Show all'
This option can be found at the bottom of the drop-down menu on the message page. By clicking on 'Show all', you go to your complete message overview.

Step 4. Click on 'More'
You'll find this option above your list of messages on the left side of your screen. Clicking on this will bring up a drop-down menu.

Step 5. Click on 'Archived'
This will open the archived messages folder, from which you can start deleting messages.

Step 6. Click on a conversation you want to delete
Click on one of the conversations on the left side of your screen. By clicking on a conversation, the conversation opens in the middle of your screen.

Step 7. Click on the gear icon in the top right corner of the message
This opens a drop-down menu with options specific to the open message.

Step 8. Click on 'Delete Conversation'
When you click on this, a pop-up will appear asking if you are sure you want to delete the conversation.
If you don't want to delete the conversation yet, but also no longer want to receive notifications, you can also choose to just turn off the notifications. You do this by choosing the 'Mute conversation' option in the drop-down menu

Step 9. Click 'Delete Conversation' in the pop-up window
This confirms that you want to permanently remove the conversation from your message overview.
Tips
- If you delete a message or conversation from your archived messages, it will only be removed from your message overview. So it will still exist in the message overview of your conversation partner, unless he or she also deletes it.
- The Facebook mobile app and Facebook Messenger do not allow you to delete archived messages. You really need to open the Facebook website to do this.
Warnings
- After you delete a message from your archived messages, there is no way to retrieve the message or conversation.
- If you use mobile data to visit the Facebook website, you may be charged on your phone bill.