What to Read on Tasbeeh When Someone Dies in Islam

According to majority of Scholars on the view of reciting Quran-al-Majeed on the Dead is – it Does Not reach them.

Abu Huraira reported: The Messenger of Allah, peace and blessings be upon him, said, “When the human being dies, his deeds come to an end except for three: ongoing charity, beneficial knowledge, or a righteous child who prays for him.”

Source: Sahih Muslim 1631

It is known that death puts a stop to all deeds, the Messenger (peace and blessings of Allah be upon him) explained that these deeds do not stop. With regard to the living, there is no doubt that he will benefit from charity given by himself or by others, and he will benefit from dua. If a person makes dua and charity for his parents whilst they are still alive, they will benefit from his dua and charity.

So it is better for the believer not to read Quran-al-Majeed for either the dead/alive or to offer salah or fast voluntarily on their behalf, because there is no evidence for any of these things. The basic principle regarding acts of worship is to refrain from everything except that which is proven to be enjoined by Allah Azza-wa-jal or by His Messenger (peace and blessings of Allah be upon him).

Secondly, 

If you mean which Surah to read while offering funeral prayer of a died person, it is Surah Fatiha (The Opening Surah) which is first surah in the Holy Quran. Beacuse:

“There is no prayer for the one who does not recite the Opening of the Book [i.e., al-Faatihah].” (Narrated by al-Bukhaari, 714).

Funeral prayer is also a prayer (Salah) in general. And most of the scholars are agreed that Surah Fatiha must be read in funeral prayer as it is read in normal salah.

However, if you meant reading Quran to dedicate a died person (known as “Quran Khuwani”), it is not true according to the true teachings of Islam.

However, if sons/daughters of died person recites the Holy Quran, it will be a blessing for that person.

So reciting Quran for a died person by other people except his children can’t benefit him.