James is implying that Gentiles know how important these rules are because Jews preach them in every city where there is a synagogue. It also implies the Gentiles can go to the teachers from the synagogues to learn more about these rules. (See: [[rc://en/ta/man/jit/figs-explicit]])
Here "Moses" represents the law of Moses, and so does "he." This can be stated in active form. Alternate translation: "The law of Moses has been proclaimed ... the law is read" or "Jews have taught the law of Moses ... they read the law" (See: [[rc://en/ta/man/jit/figs-metonymy]] and [[rc://en/ta/man/jit/figs-activepassive]])