Are the Fajr, Dhuhr, Asr, and Maghrib prayers valid after performing ghusl from janabah and repeating the prayers, given that the intention for ghusl was forgotten during the initial purification? And what is incumbent upon her?

If someone prays while in a state of impurity (حدث), they are required to repeat the prayer by scholarly consensus, even if they forgot. The ritual bath (ghusl) for major impurity (janabah) is not valid without intention (niyyah), based on the Prophet Muhammad's (peace be upon him) saying: "Indeed, actions are by intentions." So, whoever performs ghusl with the intention of removing janabah, their prayer is valid. However, if someone performs ghusl for cleanliness and only remembers the janabah after the ghusl, they must repeat both the ghusl and the prayer.