How can I delete Facebook messages I’ve sent to other Facebook users from their inbox?

No, sent messages can’t be unsent or removed from the recipient’s inbox. Depending on the persons’s notification settings, they may also receive your message as an email notification.

Source: Facebook Help Centre

Using “delete” in the messenger deletes the message in your version of the thread but not the recipient’s. So deleting a message or conversation from your inbox won’t delete it from your friend’s inbox. It isn’t possible to delete sent or received messages from a friend’s inbox.

However there is some workaround is to mark the message as Spam or Abuse (in Actions), then delete it from your messages, and disable/deactivate your account (and re-activate it after few hours), so both people won’t see it.