Are the missed prayers that a Muslim makes up for before Fajr or after sunrise sufficient as a substitute for Qiyam al-Layl (night vigil prayer) or Duha prayer?

Making up missed (obligatory) prayers does not take the place of supererogatory prayers. Rather, it is the fulfillment of (obligatory duties) that are due, and one must hasten to perform them. It is better than engaging in supererogatory prayers, due to the Prophet's (peace and blessings be upon him) saying: "My servant does not draw near to Me with anything more beloved to Me than what I have enjoined upon him." The jurists have differed regarding someone who has missed prayers: should he perform supererogatory prayers along with making up the missed ones, or should he focus on making up the missed ones? Some are of the opinion that he should perform the regular supererogatory prayers (rawātib) and that absolute supererogatory prayers are disliked. Others hold that one should not engage in supererogatory prayers instead of making up the missed ones. Some have differentiated between missing prayers due to an excuse and missing them without one.