Is one excused who forgets a prayer for part of its time, then remembers it when there is not enough time left to perform it as an on-time prayer? And is one excused who believes there is ample time left to perform the prayer, then the call to the next prayer is given, and is thus considered to have forgotten?

The jurists have unanimously agreed on the impermissibility of delaying prayer beyond its prescribed time without a legitimate excuse. However, if one delays it assuming the time remains, and then it becomes clear that the time has elapsed, or due to forgetfulness, then they are excused and incur no sin. This is based on the Almighty's saying: "And there is no blame upon you for that in which you have erred, but [only for] what your hearts intended. And ever is Allah Forgiving and Merciful."