What is the ruling on someone who intended to pray Dhuhr, then realized a week later that it was the Asr prayer, knowing that he prayed Maghrib and Isha?

The intention for a specific prayer is an obligatory part of the prayer, due to the Prophet's (peace and blessings be upon him) saying: "Deeds are only by intentions, and every person will have what they intended." So, whoever intended a prayer other than the specific one, must repeat it immediately and is not permitted to delay it, due to the Prophet's (peace and blessings be upon him) saying: "Whoever forgets a prayer, let him pray it when he remembers it, for there is no expiation for it except that."