You should bear in mind these two important matters, which are from the bounty of Allah that He has bestowed upon His slaves.
The first is that Allah, may He be exalted, says (interpretation of the meaning): “And We have indeed made the Quran easy to understand and remember, then is there any that will remember (or receive admonition)?” [al-Qamar 54:17].
The second is that the Prophet (blessings and peace of Allah be upon him) said: “The one who is skilled in reciting Qur’an will be with the noble, honourable scribes and the one who recites Qur’an and falters therein, and finds it difficult, will have a double reward.”
Narrated by al-Bukhaari (4937) and Muslim (798).
An-Nawawi (may Allah have mercy on him) said:
The one who falters is the one who stumbles in his recitation because of his poor memorisation. He will have a double reward: the reward for reciting and the reward for faltering in his recitation and the difficulty he encounters.
If we learn that the Qur’an is easy to remember and understand, and we learn that the one for whom any of that is difficult to learn, memorize or understand will have a double reward – once this is established, it will be appropriate for the wise person to strive his utmost to achieve that and to show patience in seeking to attain this sublime goal. How often has Allah made it easy for non-Arabs who do not speak Arabic well to memorize His Book in its entirety. To achieve this great virtue it is worth spending a great deal of time and competing with others.
One of the things that help one to memorize the Book of Allah, may He be exalted, is listening to it often on recordings. If it is easy for you to memorize it in this way, then you will become one of those who have memorized the Book of Allah, attained that goal and earned the reward and status of the hafiz, by Allah’s leave. The individual’s precision in recitation, memorization and acting upon the Holy Book and its rulings and teachings will determine his reward and his status before Allah, if he is sincere in his intention and seeks reward with Him.
However it is better to combine two things in that regard: striving to recite it and to memorize whatever you are able to whilst looking at the Mushaf, so as to attain the virtue of reading it yourself and the virtue of looking in the Mushaf. Then by listening to a recording of the Qur’an you will be able to do two things: correct your recitation and make sure that you have got it right before memorizing it, and then continue revising it and reminding yourself of what you have memorized after that.
Undoubtedly the one who listens to the recitation by his shaykh or teacher directly will learn the Book of Allah more precisely than the one who listens to it from a recording. The Muslim cannot memorize properly unless he learns directly from a shaykh and attends his classes whenever he can.
But for the one who does not have access to a shaykh but does have access to a recording, there is nothing wrong with him listening to it and memorizing in that manner.
And Allah knows best.