Does the reward for listening to the Qur’an with contemplation and the intention that the reward be for the deceased mother reach her?

There is no doubt that listening to the recitation of the Holy Qur’an is among the acts of devotion and worship for which the listener earns reward. It is permissible for a Muslim to dedicate the reward of any act of devotion he performs to a living or deceased Muslim. Therefore, it is permissible for your mother to listen to the Qur’an and dedicate the reward thereof to her deceased, just as it is permissible for her to supplicate for them.