What is the ruling on someone who hears the call to prayer for the next prayer time while performing an obligatory or supererogatory prayer: is their prayer valid, or must it be made up?

If an obligatory prayer is begun before the time for the next prayer enters, it is considered performance (adaa’). If it is begun after the time for the next prayer enters, it is considered making up (qadaa’). In both cases, it is necessary to complete it. It is not permissible to delay a prayer beyond its optional time except for a legitimate excuse.

As for starting a supererogatory prayer during a prohibited time, it is not validly commenced. It is obligatory to discontinue it during a time of prohibition, and recommended to discontinue it during a time of dislike (karaha). There is no make-up for it. However, if the time for starting the supererogatory prayer is not a prohibited time, then there is no harm.