Megilla 29b-
The Mishna Brura (135, 8) writes that in the days of Moshe Rabenu, it was instituted to complete the public reading of the entire
Torah. From the context, it is implied that the institution was on an annual basis. However, our Gemora teaches that in Eretz Yisroel, the Torah-reading was not completed every year but rather every three years. Is the Mishna Brura not being precise in his description of the the institution? Would it be absurd to suggest that the institution from the days of Moshe to complete the Torah-reading every year was only for Jews of the diaspora?I could not find any indication in the context of the Mishnah Berurah that you quoted that implies that the original Takanah was a one-year cycle. Rather, the Mishnah Berurah is just showing that there is an obligation to read the entire Torah with a Tzibur, from beginning to end, without skipping any Parshah. This is the practice of all places, no matter what cycle (one-year or three-year) that they use.
Kol tuv,
Mordecai