Can the reward of the recitation of the Qu'ran be granted to a living person?

A Muslim can help his Muslim brother in many ways. Some of these helps can be material; the better and effective ones are spiritual. For instance a Muslim, in his prayers, wants his brother to be pardoned, his sins to be forgiven and his brother to reach Allah's satisfaction. The prayer we make during tahiyyat which means "O Allah! Pardon me, my parents and all of the believers" is a kind of help; our Prophet (PBUH), who said the best help a Muslim can give his brother was to pray for him when he was not there, advised that believers should support each other spiritually. On the other hand, a living person needs more mercy, prayer and sawab (reward) than a dead person. A living person is continuously in a struggle with the devil, his self and his environment. If his believer brothers help him spiritually, support him with their prayers, worshipping and sawabs, he will be more likely to win this struggle. The Qoran is the greatest mediator and supporter to that effect. What can be more pleasant than a person's prayer for his Muslim brother by making the Qoran a mediator and grant the reward of it to his brother? To imagine the nonexistence of such cooperation is like to claim that there are no spiritual connection and relation among Muslims.