All perfect praise be to Alah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.
The majority of the Muslim scholars: the Hanafii, the Hanbali, the Malikii and some of the Shafiis are of the view that dedicating the reward of a good deed to the dead is permissible and benefits them, with Allah`s permission. In this regard, Allah Said (What means): "And those who came (into the faith) after them say: Our Lord! Forgive us and our brethren who were before us in the faith, and place not in our hearts any rancour toward those who believe. Our Lord! Thou art Full of Pity, Merciful." {Al-Hashr/10}. Also, the Messenger of Allah (PBUH) said: "Seek forgiveness for your brother and pray for him to be steadfast, because he is now being questioned.” {Related by Abu Dawoud}.
Ibn Abideen, A Hanafii scholar, said "In the chapter about performing Hajj on behalf of others, our scholars (Hanafiis) stated that it is permissible for a person to dedicate the reward of a good deed, such as prayer, fast, or charity, to someone else." {Ad-Dur Al-Mokhtar, vol.2/pp.243}.
Imam Ahmad Ibn Hanbal said: "the reward of a good deed benefits the dead, as stated in the texts of Sharia in this regard, and because Muslims of every country recite the Quran and dedicate its reward to their dead, and this act isn`t disproved by any of the Muslim scholars. On the contrary, all of them have agreed on it." {Al-Mobdei` Fi Shareh Al-Moqnei`, vol.2/pp.281}.
On the other hand, some Shafii scholars are of the view that dedicating the reward of a good deed doesn`t benefit the dead. It was stated in the Fatwa of Iz Ibn Abedasalam No.(47): "Whoever does a good deed and dedicates its reward to another person: dead or alive, it doesn`t benefit the latter since Allah Said (What means): " That man can have nothing but what he strives for;" {An-Najim/39}. Therefore, if he starts the good deed with intending its reward to that dead person then it doesn`t benefit the latter, except deeds on which there is a Sharia text, such as charity, fast, and Hajj."
However, if the good deed is followed with supplicating to the dead then it benefits them, as agreed by Muslim scholars since supplication benefits the dead and the living according to the unanimous agreement of the scholars. Al-Khateeb Ash-Shirbini said: "Ibn Salah said: He should say: "O` Allah! I pray that You deliver the reward of what I have recited to (name of person), then he should implore Him to accept that good deed on behalf of that dead person." {Moghni Al-Mohtajj, vol.4/pp.111}.
In conclusion, the reward of a good deed benefits the person who does it, with Allah`s Permission, and its reward benefits the dead as well according to the view of the majority of the scholars, and if it is followed with supplication then it benefits the dead, as agreed by scholars. In fact, it is better that the doer of the good deed prays that Allah accepts its reward on behalf of the dead. And Allah Knows Best.
