Du skal oprette en underforespørgsel, der returnerer det maksimale meddelelses-id af sender_id for en given modtager og slutte den til meddelelsestabellen for at få alle andre felter:
SELECT m.*
FROM `message` AS m
INNER JOIN (SELECT sender_id, MAX(message_date) as md
FROM message WHERE `receiver_id` =1 GROUP BY sender_id) AS t
ON m.message_date=t.md and m.sender_id=t.sender_id
WHERE `receiver_id` =1