Which of the four "progressive amendments" gave women the right to vote?

It was the 19th amendment, this amendment says The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of sex. Congress shall have power to enforce this article by appropriate legislation. So the answer to your question is 19th amendment

Women finally got the right to vote in the United States due to the 19th Amendment to the Constitution. This was the culmination of many years of hard work.