The obligation to recite Habdala on Mosa’eh Shabbat applies to both men and women. Nevertheless, it is customary for the husband to recite Habdala for his wife. Even if a man had already recited Habdala in the synagogue, with the intention of fulfilling his obligation, the custom is that he repeats Habdala for his wife. Despite the fact that he had already fulfilled the Misva, he may nevertheless repeat the recitation on his wife’s behalf, and this is the accepted practice.
There is, however, a discussion among the Halachic authorities concerning the two middle Berachot of Habdala – the Beracha of "Besamim" (over spices) and the Beracha of "Ha’esh" (over fire). It is unclear whether the husband may repeat these Berachot for his wife after he had already fulfilled his obligation. Therefore, Hacham Ovadia Yosef rules that in such a case, the women herself should – if she is capable of doing so – recite the Berachot of "Besamim" and "Ha’esh." This means that the husband begins Habdala and recites the Beracha over the wine ("Ha’gefen"), at which point the wife recites the Berachot over the Besamim and the fire. The husband then recites the concluding Beracha of "Hamabdil" and drinks the wine. Hacham Ovadia adds that in such a case the husband should not answer "Amen" to the wife’s Berachot of "Besamim" and "Ha’esh." It is forbidden for him to interrupt in between the recitation of the Beracha over the wine ("Ha’gefen") and his drinking the wine after reciting the Beracha of ‘Ha’mabdil." Therefore, he may not answer "Amen" to his wife’s Berachot over the spices and the fire, which do not pertain to his recitation.
If the wife is unable to properly recite these Berachot, then, according to Hacham Ovadia, the husband can and should recite the entire Habdala on her behalf, including the Berachot of "Besamim" and "Ha’esh," even though he had already recited them in the synagogue. Hacham Ovadia takes this position in his work Yabia Omer (vol. 4).
Summary: Both men and women are included in the obligation of Habdala, though it is customary for the husband to recite Habdala for his wife. If the husband recited Habdala in the synagogue with the intention of fulfilling his obligation, then when he returns home he recites the Berachot of "Ha’gefen" and "Ha’mabdil" for his wife, and the wife herself recites the Berachot of "Besamim" and "Ha’esh." The husband should not answer "Amen" to the wife’s Berachot. If the wife is unable to recite these Berachot, then the husband recites the entire Habdala service for her.
