Anyone not obligated in something cannot enable another to fulfil that obligation.
A deaf person, an imbecile and a minor are exempt [from the mitzva of Shofar]. And even if the deaf person is able to speak, the fact that he cannot hear means he has no obligation. GLOSS: However, a dumb person is able to enable others to fulfil their obligation (Beit Yosef).
A woman is exempt [from the mitzva of shofar] as it is a positive time-bound mitzva.
An Androgynous enables others of their gender to fulfil their obligation, but a Tumtum is unable to do even this.
Someone who is part servant and part free can't even enable themselves to fulfil the obligation. They require a freeman to blow for them.
Even though women and exempt, they are permitted to blow. So too, even after a man fulfilled his obligation, he is still able to blow for their obligation. However, [in these cases,] they should not make the blessing, nor should he make the blessing for them. GLOSS: And [our] custom is that women make blessings on positive time-bound mitzvot, so here too they would make the blessing for themselves. However, others should not bless for them if they have already fulfilled their obligation and are only blowing for the sake of women. However, if they are blowing [for women and] a man who is obligated, they make a blessing on his account, even though they already fulfilled their obligation, as has been explained in Chapter 585, subsection 2 in the first gloss.
המודר הנאה מחבירו מותר לתקוע לו תקיעה של מצוה ודוקא שהוא תוקע מאליו להוציאו אבל אם אמר לו המודר תקע והוציאני אסור: הגה ואם אמר קונם תקיעותיו עלי בכל ענין אסור: (ר"ן):
Someone who is engaged in blowing a shofar in order to practice doesn't fulfil his obligation. Similarly, someone who hears shofar from someone such a person doesn't fulfil his obligation. Similarly, someone who is blowing the shofar to make music and doesn't intend for the mitzva of blowing the shofar doesn't fulfil his obligation. If the listener intends to fulfil the mitzva but the blower doesn't have intent for him or if blower has intent for him but the listener does not; he doesn't fulfil his obligation until the two of them have intent, the listener and the blower.
מי שתקע ונתכוין להוציא כל השומע תקיעתו ושמע השומע ונתכוין לצאת ידי חובתו אע"פ שאין התוקע מתכוין לפלוני זה ששמע תקיעתו ואינו יודעו יצא שהרי נתכוין להוציא לכל מי שישמענו לפיכך מי שהיה מהלך בדרך או יושב בתוך ביתו ושמע תקיעו' משליח צבור יצא אם נתכוין לצאת שהרי ש"ץ מתכוין להוציא את הרבים ידי חובתן: