Is it permissible to memorize the Holy Quran for a worldly reason, namely to benefit from the Imam's residence, knowing that the primary motive for memorization is to benefit from the house? And does this action fall under the hadith: "Whoever learns knowledge by which the Face of Allah is sought, but he learns it only to gain some worldly benefit thereby, will not find the fragrance of Paradise on the Day of Resurrection"?

If the motivation for memorizing the Qur’an is worldly gain, then this falls under the warning mentioned in the Hadith: "Whoever learns knowledge by which the Face of Allah is sought, but he does not learn it except to acquire therewith a worldly عرض (gain/benefit), will not smell the fragrance of Paradise on the Day of Resurrection." And His (Allah's) saying, the Most High: {Whoever desires the life of this world and its adornments - We will fully repay them for their deeds therein, and they will not be deprived therein. Those are the ones for whom there is nothing in the Hereafter but the Fire. And worthless is what they did therein, and futile is what they used to do.} This action is considered a form of shirk (polytheism), and repentance from it is obligatory. It is recommended to memorize the Qur’an with the intention of drawing closer to Allah, for by doing so, one attains the reward of both this world and the Hereafter, based on His (Allah's) saying, the Most High: {Whoever desires the reward of this world - then with Allah is the reward of this world and the Hereafter.}