The Shulchan Aruch states that the requirement of Havdalah is a Torah obligation, just like Kidush. It is a mitzvah that applies equally to men and women. Therefore, since women are obligated in this mitzvah, a man is allowed to recite Havdalah for a woman even if he had already recited or heard Havdalah.
This is the ruling of the Chida (a”h), in His sefer, Birkeh Yosef. However, since some chachamim dispute this ruling, Ha’Rav Bentzion Abba Shaul (a”h) and Ha’Rav Ovadyah Yosef (a”h), ruled that it is preferable for a husband to have in mind not to fulfill his Havdalah obligation in shul. This way, he can recite Havdalah for his wife according to all opinions.
In a case where the husband had already recited Havdalah in shul and now recites Havdalah for his wife, the wife should recite the berachah over the besamim. Since the husband is not required to smell besamim, reciting the berachah over the besamim could constitute a hefsek (interruption) between the berachah over the wine and his drinking the wine. Therefore, the wife should recite the berachah over the Besamim. She should also recite the berachah over the flame.
There is great controversy among halachic authorities as to whether women are obligated to recite this berachah of, “Bore Me’oreh Ha’esh.” The Chafetz Chaim (a”h) writes that women are likely not included in this obligation, whereas others, including the Chida, Rav Chaim Palachi (a”h) and Ha’Rav Ovadyah Yosef, disagreed, and maintained that women are included in this obligation just like men. In any case, Ha’Rav Ovadyah Yosef ruled that it is preferable for the wife to recite the berachah over the flame if her husband had already fulfilled his requirement.
It turns out, that if a husband fulfills his requirement in shul and then recites Havdalah for his wife, he recites “Boreh Peri Ha’gefen,” and then the wife recites the berachot over the besamim and the flame. The husband then recites “Ha’mavdil” and drinks the wine. The husband does not answer “Amen” to the wife’s berachot over the besamim or the flame (Yabia Omer, 4:23-24).