Deleted Facebook messages are a big problem especially when you want them back, unfortunatelly there is no exact way to get them back.
Inagine that you have deleted a message and want that specific message back.
There is some way to get deleted Facebook messages back but no guaranteed.
Check your archived messages
You may archived that specific message and fin it.
Check is it e-mailed or not
According to your settings, Facebook send mails to your e-mail if your account’s settings set up as mailed me when get messages. In those cade you could see the message.
Ask the Other person for a copy
Messages occur between at least 2 people when you delete a message it means you deleted it from your account not the reciver’s, so if you ask for a copy most probably you will get your deleted message back.