Is it permissible to perform nighttime prayers (Qiyam al-Layl) for a week with the intention of achieving a worldly matter, knowing that one will later continue performing nighttime prayers for the sake of the Afterlife, and that this worldly matter brings one closer to Allah?

There is no objection to performing night prayers (Qiyam al-Layl) and supplicating to Allah Almighty for what benefits the servant in their religion and worldly life. The virtue of Qiyam al-Layl is immense, and it is a time when supplications are answered. Several hadiths have been narrated from the Prophet, peace and blessings be upon him, illustrating the virtue of supplication in the latter part of the night, such as the hadith of the Divine Descent to the lowest heaven, and the hadith about the hour in which no Muslim supplicates to Allah for good but that He grants it to him. It is best for the servant's intention in performing Qiyam al-Layl to be to attain Allah's pleasure and success in the afterlife. However, if this is combined with the intention of fulfilling a worldly need, there is no harm, especially if that need brings one closer to Allah. But if the intention is solely limited to worldly matters, this is a deficiency. The Prophet, peace and blessings be upon him, pointed to the virtue of those who perform Qiyam al-Layl out of desire for what is with Allah and fear of what is with Him.