Will the reward for memorizing the entire Qur’an be written for someone who sincerely intended to memorize it and began doing so, then passed away before completing it?

There are differences between determination ('azm) and mere intention (niyyah). A firm determination to do good deeds is rewarded like the reward of one who performs them, especially if one starts the work and is then unable to complete it. The noble Prophetic tradition indicates that whoever intends a good deed but does not perform it, a complete good deed is written for him. If he performs it, ten good deeds are written for him, up to seven hundredfold, or many more folds. Among the proofs for this is what is mentioned regarding the virtue of the capable person who is unable (to act), such as the saying of the Prophet, peace and blessings be upon him: "Indeed, in Madinah are men who, no journey you traveled nor any valley you crossed, but they were with you." They said, "And they are in Madinah?" He said, "And they are in Madinah, for the excuse detained them." Likewise, the hadith of Abu Kabshah al-Anmari concerning the equality of reward between the rich person who performs good deeds with his wealth and the poor person who sincerely wished to perform them. As for the sincere and confirmed intention from which the action does not fall short except due to inability, this firm will grants its owner the full reward of the doer.

As for whoever strives by the means of a good deed but does not achieve it, a full reward is written for him, like one who sets out to migrate to Allah and His Messenger then death overtakes him; his reward is due from Allah.