Does One Have to Make up Missed Prayers in the Times of Similar Current Prayers?

No, it is not necessary for one to make up the missed prayers (qadha) in the times of similar current prayers (such as making up a previous Fajr in the time of Fajr); rather, one is allowed to make up the prayers at any time during the night or day, except at three times.

It is stated in al-Fatawa al-Hindiyya:

“There are three times when it is not permissible to offer any obligatory (fardh) prayers, the funeral prayer and the prostration of recital (sajda al-Tilawa). These times are: When the sun rises up (until it is above the horizon by the length of a spear, about twenty minutes after sun rise), when the sun is at its zenith until it begins to move, and when the sun turns red until it sets (about twenty minutes to half an hour before sun set)……It is not permissible in these three times to offer any make up prayers for the obligatory (fardh and wajib) prayers that were missed.” (al-Fatawa al-Hindiyya, 1/52)

Therefore, it is perfectly okay for you to make up a previous Fajr prayer in the time of Zuhr Salat for example, or to perform the Qadha of Maghrib prayer in the middle of the night. It is not necessary to perform each Qadha prayer in the time of its equivalent current prayer. However, one must avoid making up any prayers in the three times mentioned above, for offering them in those times is impermissible hence they will be considered invalid.

And Allah knows best