Is it permissible for a Muslim to pray that the reward for his good deeds be divided equally between him and his deceased parents throughout his life?

There is no impediment to supplicating with the aforementioned supplication. The deceased will receive a reward similar to that of the deed performed, according to the Shafi'is and a group of scholars, and a reward identical to that of the deed performed, according to the Hanafis and a group of scholars. Imam Al-Qarafi holds that acts of worship are of three types: a type whose reward cannot be transferred to anyone other than its doer, such as faith; a type whose reward is unanimously agreed upon to be transferred to the deceased, such as financial acts of worship; and a type about which there is disagreement, such as fasting, Hajj, and reciting the Qur'an. The majority opinion is that the reward for recitation reaches the deceased, but the Shafi'is believe that a similar reward reaches them, while the Hanafis believe that the identical reward reaches them.