You can delete individual messages or a full conversation directly from the Messenger app. Tap and hold the message or photo you'd like to delete.

1. Delete Facebook
Message
WWW.HOWTODELETE.ORG

2. Delete Facebook Messages using
Mobile Application
 Open Messenger application on
your smartphone.
 Tap on the sender’s image whose
message you want to delete.

3.  Find the message you want to
delete and then tap & hold the
message.
 You will see message options
at the bottom of the screen —
tap on “Bin” icon.

4.  Tap on “Remove for you” option if you
want to delete the message from your
device only. If you don’t want the
message to be displayed on receiver’s
end as well then tap on “Remove for
everyone.” However, keep in mind
that, 10 minutes should not have
passed after you sent the message to
be able to delete the message from
the receiver’s.

5.  A confirmation message will pop up on your screen.
Tap on “Remove” to get rid of the message
permanently.

6. Delete Facebook Message using
Desktop/Laptop.
 Open facebook.com on any web browser you prefer
and log in if you are not already logged in.
 Click on message icon towards the top right corner
of the page just before the notification icon.

7.  A drop-down list will appear displaying the recent
conversation you have had. Click on the conversation
from where you want to delete a specific.

8.  The conversation you have selected will be displayed
in a pop-up message box at the bottom of the
screen.
 Find the message that you want to delete and then
click on the menu icon (…). Now click on Remove.

9.  A sub-window will pop up requiring you to confirm
that you choose to get rid of the message
permanently. Choose from option to “Remove for
Everyone” or “Remove for You”. Finally, click on
“Remove” and you will get rid of the message
permanently.

10. Delete entire conversation
Using Desktop
 Open Facebook.com in any web browser. Log in
using the username and password of the account
from where you want to delete the conversation.


11.  Click on the message icon towards the top right
corner of the page just before the notification icon
and open the conversation that you want to delete.

12.  Once you open the conversation in a message box
that appears at the bottom of the screen; click on the
“Option” (gear icon).

13.  A drop-down menu will appear. Scroll down to the
end of the list and then click on “Delete
Conversation.”

14.  Facebook will notify you that once you delete the
conversation, it cannot be undone. Click on “Delete
Conversation” to get rid of the conversation
permanently.

15. Delete Facebook message from
messenger
 Open Facebook messenger.
 Find the conversation that you
want to delete.
 Tap and hold the conversation.
 You will see some options at the
right of the conversations. From
among the options tap on “Delete
icon” (red bin icon).

16.  A confirmation message will
pop up. Tap on “Delete” and
Facebook will delete the
conversation permanently.

17. Source:
https://howtodelete.org/delete-facebook-message/