Siman 594

One who did not hear the blasts—another who has already blown may blow for him, according to the law of all mitzvot, that even though he has already fulfilled his obligation, he may fulfill the obligation of others. He may also recite the blessing on his behalf, as in kiddush and havdalah. However, one who did not recite the blessings of Malchuyot, Zichronot, and Shofrot, or who did not pray at all—his fellow cannot fulfill the obligation for him. Specifically, the shaliach tzibbur fulfills the obligation for others, because that is in public. But an individual for an individual—he does not fulfill the obligation for him in prayer, even if he himself also needs to pray. For an individual does not become an agent for his fellow to fulfill his obligation in prayer, whether on Rosh Hashanah and Yom Kippur, or during the rest of the year, unless it is with ten, where the shaliach tzibbur fulfills the obligation.

And that which our sages, of blessed memory, said (Berakhot 45b): A scribe blesses, and an unlearned person fulfills his obligation—this is regarding Birkat HaMazon and the blessings of the mitzvot, and not regarding the prayer which was established in a whisper. And no individual has permission to make his voice heard and fulfill the obligation of others until he descends before the ark. And thus Rav Sherira Gaon sent (Tur), and so wrote the Rambam in the fourth chapter of Tefillah. Nevertheless, some say that if one is unable to pray—his fellow fulfills the obligation for him with his prayer, for specifically for one who is able to pray for himself he cannot fulfill the obligation, but not for one who is unable. And one may rely on this in a time of pressing need.