It is clear from the Mishna and Gemara in Masechet Berachot that women are included in the obligation of Birkat Ha’mazon, and this obligation is codified in the Shulhan Aruch (Orah Haim 186). It is unclear, however, whether women are required to recite Birkat Ha’mazon on the level of Torah obligation, or only Mi’de’rabbanan (by force of Rabbinic enactment). The Gemara addresses this question, but, according to many Rishonim (Medieval Halachic scholars), it does not reach a conclusion. Indeed, the Shulhan Aruch cites both views, without reaching a definitive ruling regarding women’s status vis-à-vis Birkat Ha’mazon.
The practical implications of this question relate to the issue of whether a woman can recite Birkat Ha’mazon on behalf of a man so he can fulfill his obligation through her recitation. In the case where a man ate to the point of satiation, such that he is required to recite Birkat Ha’mazon on the level of Torah obligation, he should not fulfill his Misva by listening to his wife’s recitation. Since she might be obligated on a lower level of obligation, she cannot recite Birkat Ha’mazon for him. However, if the man ate a Ke’zayit but less than the amount of satiation, in which case he is required to recite Birkat Ha’mazon only Mi’de’rabbanan, then his wife may, strictly speaking, recite Birkat Ha’mazon for him and he can fulfill his Misva by listening to her recitation.
A number of Aharonim (later Halachic authorities) raise the question of how a woman can recite the words "Ve’al Beritecha She’hatamta Bi’bsarenu Ve’al Toratecha She’limadetanu" in the text of Birkat Ha’mazon. In this phrase we give thanks to Hashem for giving us the Misva of Berit Mila and the Misva of Torah learning, through which we earn the merit of Eretz Yisrael. Women, of course, do not have the Misva of Berit Mila and are not commanded to study Torah. How, then, can a woman recite this phrase? Indeed, the Rama (Rabbi Moshe Isserles of Cracow, Poland, 1525-1572), in his glosses to the Shulhan Aruch (Orah Haim 187), rules that women omit this phrase, since they are not included in these Misvot. This ruling gives rise to the question of how a woman can recite Birkat Ha’mazon on behalf of a man. Since there is a portion of the text that she must omit, it is difficult to understand how a man can fulfill his obligation of Birkat Ha’mazon by listening to his wife’s recitation.
Sure enough, Maran, in Bet Yosef (187), disagrees with this position, and rules that women do, in fact, recite the phrase of Berit Ve’Torah. He bases his ruling on the concept that a man becomes complete only once he is married, at which point the husband and wife become a single entity and like one body, as the Torah says, "Ve’hayu Le’basar Ehad" ("they become like one flesh" – Bereshit 2:24). The woman is therefore able to thank Hashem for the Misvot of Berit and Torah because she is part of the same entity as her husband, who is, of course, included in these Misvot. Moreover, women are obligated to learn the portions of Torah that bear practical relevance to them, and the concept of the Berit Mila also applies to them insofar as they are part of the Jewish Nation, even if they obviously do not undergo circumcision.
Indeed, the Mishna Berura (Rav Yisrael Meir Kagan, 1839-1933) observes that the common practice is for woman to recite the entire text of Birkat Ha’mazon, including the passage of "Berit Ve’Torah." This is also the ruling of several other authorities, including the Hid"a (Rav Haim Yosef David Azulai, 1724-1807) and the Kaf Ha’haim (Rav Yosef Haim Sofer, Baghdad-Israel, 1870-1939), and this is the accepted Halacha. Thus, a woman recites the full standard text of Birkat Ha’mazon, including the passage of "Berit Ve’Torah."
Summary: Women are included in the obligation of Birkat Ha’mazon, and they recite the same full text as men. Technically speaking, a woman can recite Birkat Ha’mazon on a man’s behalf, unless the man had eaten an amount requiring Birkat Ha’mazon on the level of Torah obligation (meaning, to the point of satiation), in which case he should not fulfill his obligation by listening to a woman’s recitation.