The Quran

إِنَّ اللَّهَ وَمَلائِكَتَهُ يُصَلّونَ عَلَى النَّبِيِّ ۚ يا أَيُّهَا الَّذينَ آمَنوا صَلّوا عَلَيهِ وَسَلِّموا تَسليمًا

Ali Unal

Surely God and His angels bless the Prophet (He always treats him with His special mercy, with the angels praying to Him to grant him the highest station of praise with Him, and for the decisive victory of his Religion). O you who believe, invoke the blessings of God on him, and pray to God to bestow His peace on him, greeting him with the best greeting. (Love and follow him with utmost sincerity and faithfulness, and give yourselves to his way with perfect submission).¹

Calling God’s blessings and peace upon God’s Messenger, upon him be peace and blessings, at least once in a lifetime is incumbent upon every Muslim. And doing so at each mention of his name is a highly recommendable act. According to the Shāfi’ī and Hanbalī schools, it is obligatory in the last sitting of every Prayer (Salāh) after tashahhud, without which the Prayer is not acceptable. According to other schools, it is sunnah.
Calling God’s blessings and peace upon the Messenger, upon him be peace and blessings, is a link between him and the believers. His responsibility was extremely grave, and he is always concerned with the Muslims individually and collectively, even after his death.
So calling God’s blessings and peace upon him as a religious duty was not restricted to his lifetime. By doing so, we are also praying for ourselves, because we are both building an important connection with him and petitioning God through him to help us with our religious responsibilities.
Upon the injunction of the Messenger, upon him be peace and blessings, we must include his family and even his progeny in calling God’s blessings and peace upon him.
That the injunction of calling God’s blessings and peace upon him stays in effect even after his death, until the Last Day, signifies that praying for the dead is a valid religious act and may be of help for them.