Is it permissible to be released from a vow not to marry until memorizing the Qur'an, knowing that the memorization is not yet complete?

If you vowed to memorize the entire Qur'an before marriage, you must fulfill it because it is an act of obedience, for the Prophet, peace and blessings be upon him, said: "Whoever vows to obey Allah, let him obey Him." It is not necessary to delay marriage. If you are unable to fulfill the vow, you are obligated to perform an expiation for breaking an oath, which is feeding ten poor persons, or clothing them, or freeing a slave. If you cannot find any of these, then fasting for three days.