Is it permissible to memorize the Qur’an by writing it down, given that this method is quicker for concentration and memorization than oral instruction? And is there any objection to writing it in any notebook?

It is permissible to write the Noble Qur’an for the purpose of aiding memorization, especially if this method helps in speeding up or perfecting memorization. Attention must be paid to the purity and cleanliness of what the Qur’an is written on, and to protect it from desecration and filth.