The Shulhan Aruch (Orah Haim 266:8) rules that the requirement of Habdala on Mosa’eh Shabbat constitutes a Torah obligation, just like Kiddush, and that this Misva applies equally to both men and women, just like Kiddush. Therefore, since women are obligated in this Misva, a man is allowed to recite Habdala for a woman even if he had already recited or heard Habdala. Since the woman needs to fulfill her obligation, a man may recite Habdala for her even though he had already fulfilled his obligation.
Thus, for example, if a husband heard Habdala in the synagogue, or was the Hazan and recited Habdala there, he may recite Habdala for his wife when he comes home. This is the ruling of the Hid"a (Rav Haim Yosef David Azulai, 1724-1806), in Birkeh Yosef. However, since some authorities dispute this ruling, Hacham Bension Abba Shaul (Israel, 1923-1998), as well as Hacham Ovadia Yosef, ruled that it is preferable for a husband to have in mind not to fulfill his Habdala obligation in the synagogue. This way, he can recite Habdala for his wife according to all opinions. Nevertheless, if the husband did fulfill his requirement in the synagogue, he may recite Habdala for his wife, in accordance with the Shulhan Aruch’s ruling.
In such a case, where the husband had already recited Habdala in the synagogue and now recites Habdala for his wife, the wife should recite the Beracha over the Besamim. Since the husband is not required to smell Besamim, reciting the Beracha over the Besamim could constitute a Hefsek (interruption) in between the Beracha over the wine and his drinking the wine. Therefore, the wife should recite the Beracha over the Besamim. Likewise, the wife should recite the Beracha over the flame. There is considerable controversy among the Halachic authorities as to whether women are obligated to recite this Beracha – "Boreh Me’oreh Ha’esh" – on Mos’aeh Shabbat. The Hafetz Haim (Rav Yisrael Meir Kagan of Radin, 1839-1933), in Be’ur Halacha, writes that women are likely not included in this obligation, whereas others, including the Hid"a, Rav Haim Palachi (Turkey, 1788-1869) and Hacham Ovadia Yosef, disagreed, and maintained that women are included in this obligation just like men. In any event, Hacham Ovadia ruled that it is preferable for the wife to recite the Beracha over the flame if her husband had already fulfilled his requirement.
It turns out, then, that if a husband fulfills his requirement at the synagogue and then recites Habdala 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’mabdil" and drinks the wine. The husband does not answer "Amen" to the wife’s Berachot over the Besamim and the flame (Yabia Omer, 4:23-24).
Summary: Women are obligated in the Misva of Habdala just like men. A husband should preferably have in mind not to fulfill the requirement of Habdala in the synagogue on Mosa’eh Shabbat so he can recite Habdala for his wife at home according to all opinions. Nevertheless, if he did fulfill his requirement in the synagogue, he may still recite Habdala for his wife at home, but in such a case the wife should recite the Berachot over the Besamim and the flame.
