Is the prayer of one who is in a state of major ritual impurity (janabah) and intended to perform ghusl only for Jumu'ah prayer, but forgot the intention for janabah until he had led a full day of prayers, valid, and likewise the prayer of those who prayed behind him, and should he inform them of that?

Whoever performs ghusl (definition) with the intention of Ghusl al-Jumu'ah (Friday bath) while forgetting their major ritual impurity (hadath (definition) al-akbar), their ritual impurity is lifted according to the soundest opinions of scholars, even if they later remember that a mandatory ghusl was due on them. However, some scholars qualify this by stipulating that this applies only if they were forgetful of their ritual impurity. If they were not forgetful, then it is not lifted, because the supererogatory ghusl is not for ritual impurity. The Prophet, peace and blessings be upon him, said: "Indeed, actions are by intentions." So, if someone is aware of their state of janabah (definition) (major ritual impurity) and only intends the supererogatory ghusl, then the opinion that it suffices is questionable.