The Shulchan Aruch (O. C. 108) rules that if a person missed one of the daily prayer services, he can make up the missed Tefila after reciting the next prayer service. Thus, for example, a person who missed Shacharit recites an additional Shemoneh Esrei at Mincha to make up for the missed Shacharit service. This Halacha applies only to somebody who misses a prayer mistakenly or due to circumstances beyond his control, such as if he took ill or overslept. One who intentionally misses a prayer does not have the opportunity of making up the missed Tefila.
When a person recites Shemoneh Esrei twice to make up for a missed prayer, the first Shemoneh Esrei is recited for the current obligation, whereas the second Shemoneh Esrei serves as a make-up prayer for the missed Tefila. In the case mentioned above, the first Shemoneh Esrei recited fulfills the current obligation of Mincha, while the second Shemoneh Esrei is the make-up prayer for Shacharit.
What is the proper procedure to follow if one missed Shacharit and Musaf on Shabbat morning? Musaf can be recited the entire day, so he still bears an obligation with respect to Musaf. In addition, he must recite Shemoneh Esrei twice at Mincha, one for Mincha and the other to make up for Shacharit. In which sequence does he recite these three prayers?
Many authorities, including the Chid"a (Rabbi Chayim Yosef David Azulai, Israel, 1724-1806) in his work Birkei Yosef (108:4), the Ben Ish Chai (Rabbi Yosef Chayim of Baghdad, 1833-1909) in Parashat Mishpatim, and the Chafetz Chayim (Rabbi Yisrael Meir Kagan, Lithuania, 1839-1933), in his work Mishna Berura (108:16), rule that in this situation one should proceed as follows: he first recites the Shemoneh Esrei of Mincha for the current obligation, followed by Musaf, and he then repeats the Shemoneh Esrei of Mincha to make up for his missed Shacharit. Since he is currently obligated to recite Mincha and Musaf, these prayers should be recited before the additional Shemoneh Esrei that serves to make up for the missed Shacharit prayer.
Summary: A person who mistakenly, or due to circumstances beyond his control, did not recite one of the daily prayers makes up the missed prayer by reciting an extra Shemoneh Esrei after the next prayer service. If somebody missed Shacharit and Musaf on Shabbat morning, after the Shemoneh Esrei of Mincha he should recite Musaf followed by an additional Shemoneh Esrei of Mincha to make up for the missed Shacharit.
