Is it permissible to make up a prayer after its time has passed due to successive private lessons or being preoccupied with a trip?

Delaying prayer beyond its prescribed time due to private lessons or trips that do not permit shortening the prayer is considered a major sin. This is based on Allah's saying: "So woe to those who pray, [But] who are heedless of their prayer," and "Then, there succeeded them a generation who neglected prayers and pursued desires; so they are going to meet evil." As for delaying prayer beyond the beginning of its optional time, it is permissible, even though performing it at the earliest time is better.