Is the Friday ghusl sufficient for ghusl from janabah if the intention for it was not made, and nocturnal emission was discovered after the ghusl and after reading the Qur'an with the intention of completing it in Ramadan? What should be done regarding the prayers and recitation that have already taken place?

The state of janabah (ritual impurity requiring a full bath) is not lifted unless one intends, by their ghusl (ritual bath), to remove the hadath (state of impurity) or to permit what is not permissible without it. This is based on the Prophet's (peace be upon him) saying: "Indeed, actions are by intentions." Scholars have differed regarding a person in a state of janabah who performs a recommended ghusl: According to the Shafi'i school, their state of hadath is not lifted. However, the Hanbalis hold that if someone performs a recommended ghusl, it suffices for the obligatory ghusl if they had forgotten about it. To avoid disagreement and to clear one's conscience, it is best to repeat the prayers that were performed before the ghusl was done with the intention of removing the hadath. As for reading the Qur'an, the matter is easier, as some scholars do not prohibit a person in a state of janabah from reading.