A person who mistakenly or due to circumstances beyond his control missed the Mincha prayer on Erev Shabbat makes up the missed Mincha by reciting an extra Shemoneh Esrei at Arvit that night. Even though he missed a weekday Shemoneh Esrei, he nevertheless makes up the missed Tefila by reciting an additional Shemoneh Esrei of Shabbat Arvit ("Ata Kidashta…"). He must have in mind that the first Amida fulfills his requirement of Arvit, while the second serves to make up for his missed Mincha prayer.
If this individual serves as the Chazan for Arvit, then, according to Chacham Ovadia Yosef (as he writes in Yabia Omer, vol. 6, Orach Chayim section, Siman 19), he may make up the missed prayer through the recitation of the Beracha Me'ein Sheva, the "Magen Avot" prayer recited after the Amida of Arvit on Friday night. This Beracha is an abbreviated Amida, and according to some authorities it functions as a bona fide repetition of the Shemoneh Esrei. Chacham Ovadia therefore rules that a Chazan who had missed Mincha can make up the missed prayer through the recitation of the Beracha Me'ein Sheva. The Chazan should have in mind while reciting the Beracha Me'ein Sheva that it should serve as the make-up prayer for his missed Tefila.
Others, however, should not rely on the Beracha Me'ein Sheva for this purpose, since only the Chazan recites this Beracha. If a congregant missed the Mincha prayer and asks the Chazan to have in mind during the recitation of Beracha Me'ein Sheva that it should constitute the congregant's make-up prayer, although he has acted improperly, ex post facto he has fulfilled his make-up requirement. It is more proper, however, for a congregant in this situation to repeat the entire Amida of Arvit, rather than relying on the Chazan's recitation of the Beracha Me'ein Shalosh.
Summary: Somebody who either mistakenly or due to extenuating circumstances missed the Mincha prayer on Friday afternoon makes up the missed prayer by repeating the Amida of Arvit on Friday night, having in mind that the second Amida serves as the make-up prayer for Mincha. If this person serves as Chazan during Arvit, he can have in mind as he recites the Beracha Me'ein Shalosh ("Magen Avot…") to make up the missed Mincha prayer through the recitation of this Beracha.
See Shulchan Aruch, siman 108, Halacha 9, and Halacha Berura Helek 6, pages 49-53.
