Siman 594
Presented here for study, not as a practical ruling. The Shulchan Aruch rules by Sephardi custom, the Rema's glosses by Ashkenazi custom, and the Kitzur follows Ashkenazi custom. For a practical question, ask your rabbi.
א יָחִיד שֶׁלֹּא תָּקַע, חֲבֵרוֹ יָכוֹל לִתְקֹעַ לוֹ לְהוֹצִיאוֹ יְדֵי חוֹבָה; אֲבָל יָחִיד שֶׁלֹּא הִתְפַּלֵּל ט' בְּרָכוֹת, אֵין חֲבֵרוֹ יָכוֹל לְהוֹצִיאוֹ. הַגָּה: וְיֵשׁ חוֹלְקִין וְאוֹמְרִים דְּאִם לֹא יָכוֹל לְהִתְפַּלֵּל, חֲבֵרוֹ יָכוֹל לְהוֹצִיאוֹ בִּתְפִלָּתוֹ (רַ"ן סוֹף רֹאשׁ הַשָּׁנָה וּמָרְדְּכַי וְהַגָּהוֹת אֲשֵׁרִי ספ"ג דְּרֹאשׁ הַשָּׁנָה).
1 An individual that did not pray, his friend cannot fulfill (for him). And in it is one paragraph. An individual that does not blow shofar, his friend is able to to blow for him to fulfill his obligation. But an individual that did not pray the 9 blessings (of the Rosh HaShana Musaf Prayer), his friend is unable to fulfill (for him). Rema: There are those that argue, and say that if one is not able to pray, then his friend is able to fulfill for him with his (the friend's) prayer (Ran end of tractate Rosh HaShana, Mordechai, and Haagos Ashiri end of the first chapter of Rosh HaShana).