We think of the Prophet (pbuh) in many ways but how often do we think of him as a brother? Not just any brother, the most blessed one. The Prophet (pbuh) said that his brothers are those who believe in him but have never seen him. What about dua for your most noble brother, the Prophet?
One sahabi asked how much peace and blessings should I send on you oh messenger of Allah? The Prophet replied “If you dedicate 1/4 of your dua to offer salawat then that is good”, the sahabi asked “What if I offer half of my dua for your salawat?” The Prophet (pbuh) replied “That is good and you will be blessed”. Then the sahabi asked “What if I dedicate my whole dua to sending peace and blessings on you?” The Prophet replied “If you do this Allah will take care of all your problems and forgive all of your sins”.
When you make dua for someone else, and they do not know about it, the angel comes and says “Ameen, and the same for you too”. When we offer peace and blessings on the Prophet (pbuh) Allah sends 10 times the peace and blessings on you, Allah forgives 10 sins and Allah raises you by 10 stations. There are angels who roam the earth looking for those who send salalwat on the Prophet (pbuh) and go and convey this to the Prophet (pbuh). The Prophet (pbuh) responds to the salams we give him!