It is recommended to gift the reward of reciting the Quran to Holy Prophet (sawa), Hazrat Fatemah Zahra (sa) and the Holy Imams (as).
Ali Ibne Mughira asked Imam Kazim (as), My father had asked your respected grandfather regarding the complete recitation of Quran every night and he told him, Yes it can be completed every night. When my father asked about completion of Quran in the month of Ramadan he received the same reply. So he used to finish reading the complete Quran forty times during the holy month of Ramadan. After him I continued this practice. On the day of Eid, I complete a Quran for the Holy Prophet (sawa) and after him for Ameerul Momineen (as) till I reach you. So tell me how do you consider this act? Imam (as) said, Your reward is that you shall be in the company of those exalted personalities. The narrator said, Such a high reward? Imam (as) said thrice – Yes. (Beharul Anwar volume 98 chapter 5 page 5)
We beg to the Almighty Allah for the sake of Mohammed and his progeny, to give us all tawfeeq (opportunity) to perform this meritorious deed.