What is the ruling on making up invalid prayers due to a breach of the condition of purity or intention, according to Sheikh Al-Islam Ibn Taymiyyah? Is re-performing the prayer obligatory for someone who intentionally prayed an invalid prayer and its time has expired? Is it obligatory to make up the prayer if the worshiper forgot to wash a part of his body during ghusl and remembered it after the prayer time had expired? Is it permissible to make up one day's prayers with each (subsequent) day for those who hold the view that making up (missed prayers) is obligatory?

The Gist of the Fatwa:

Ibn Taymiyyah held the view that one who intentionally misses a prayer is not required to make it up but should perform many supererogatory prayers. However, the majority opinion, which is more cautious and absolves one of responsibility, is that intentionally missed prayers are a debt owed by the one who left them, and repentance and re-performance are obligatory upon him. Therefore, whoever intentionally performed a prayer incorrectly, such as one who intentionally neglected purification, or did not make an intention deliberately, or prayed without performing ghusl (ritual bath) from major impurity, must repent and make up the prayer.

If someone forgot to wash a part of their body after ghusl and after the prayer and the time for it passed, they must make up all the prayers they performed with that incomplete ghusl after washing the forgotten part or re-performing the ghusl completely, according to the differing opinions of the jurists.

Whoever has missed many prayers must make them up immediately. It is preferable to make up two days' worth of prayers or more in a single day, as long as it does not affect his ability to provide for his dependents.