Is it permissible for a person to dedicate the reward of reciting the the Qur'an to a living person, and does that affect their own reward?

Donating the reward of reading the Qur'an to another person is permissible, whether that person is alive or deceased. The entire reward is transferred to the one for whom it is dedicated. The donor may also be rewarded for their love for their brother and their kindness towards him.