When does a boy reach full puberty, and is this son held accountable for the prayers he missed and the wrong practices he engaged in if he experienced seminal discharge without a wet dream during the period of puberty?

The emission of semen, whether in sleep or wakefulness, is a sign of puberty by scholarly consensus, based on the Almighty's saying: "And when your children reach puberty, let them ask permission," and the Prophet's (peace be upon him) saying: "The pen has been lifted from three: from the child until he reaches puberty." Puberty also occurs upon reaching 15 lunar years of age, and by the growth of coarse hair around the private parts. If a boy masturbates and semen is emitted, then he has reached puberty, and the pen of responsibility has been applied to him. He must make up for any prayers he missed after reaching puberty.