You can’t delete a Messenger conversation from the other person’s phone. Deleting a chat only removes it from your side, while “unsend” can remove your own message for everyone if it’s still available.

What you can do

  • Delete the conversation: removes it only from your inbox. The other person still keeps it.
  • Unsend a message you sent: removes that specific message from both sides.
  • You cannot remove messages the other person sent from their chat.

Steps for one message

  1. Open the chat.
  2. Long-press your message.
  3. Tap Delete or Remove.
  4. Choose Unsend or Delete for everyone if that option appears.

Important note

If the message was sent a while ago, the unsend option may no longer be available.

Plain answer

If your goal is to erase the whole conversation on the other end, Messenger does not let you do that. The closest option is unsending your own messages one by one, when allowed.

TL;DR: You can delete it only from your side; you can unsend only your own messages, not the other person’s.