What should one do who has missed many prayers due to a legitimate Shar’i excuse, some of which are recorded and some of which are not recorded and whose number he does not remember, and how can they be made up given the time constraint?

Prayer is an obligatory duty and a pillar of Islam. It is the first thing a servant will be questioned about on the Day of Resurrection. It is not permissible to perform it before or after its appointed time except for a legitimate excuse, such as combining prayers during travel or illness. Abandoning prayer is not a light matter, and a Muslim must repent and make up for the prayers they have missed. A Muslim makes up for missed prayers by striving to estimate the number of prayers they believe they missed, and they are restricted to making up only the obligatory prayers, not the supererogatory or Sunnah prayers, unless there is specific evidence for the latter.