Praise be to Allah.
Reciting al-Fatihah for the deceased
There is no evidence for reciting al-Fatihah or any other part of the Quran and giving (the reward for) it to the deceased. We must not do that, because it was not narrated that the Prophet (peace and blessings of Allah be upon him) or his Companions (may Allah be pleased with them) did any such thing.
What benefits the dead?
It is prescribed to make du`a for the deceased Muslims and to give charity on their behalf by giving to the poor and needy. In this way, a person may draw closer to Allah and ask Him to give the reward for that to his father, mother or other people, deceased or alive.
The Prophet (peace and blessings of Allah be upon him) said: “When a man dies, all his deeds come to a halt apart from three: ongoing charity (sadaqah jariyah), beneficial knowledge or a righteous child who will pray for him .”
A man said to the Prophet (peace and blessings of Allah be upon him): “O Messenger of Allah, my mother has died and she did not make a will. I think that if she had spoken she would have given in charity. Will she be rewarded if I give in charity on her behalf?” He said, “Yes.” (Sahih – agreed upon)
The same applies to Hajj and `umrah on behalf of the deceased and paying off his debts . All of these actions will benefit him, as was narrated in the shar’i evidence. But if the questioner is referring to treating the family of the deceased person kindly by giving them money or meat (i.e., food), there is nothing wrong with that if they are poor.
And Allah knows best.