Being that Schach has to be put down L’shem the Mitzvah of Succah, is it permissible for a woman to lay the Schach and have this in mind, even if a woman os not M’chuyev in Succah?
The schach does not have to be put down L’shem the Mitzvah of Succah but requires L’shem Tzel so therefore a women can also do it. Never the less the Poskim write that lechatchilah a woman should not put down the schach because of Rabenu Tam who holds that someone who is not obligated in a mitzvah cannot perform the mitzvah.
O:CH 635:1 @ Mishnah Berurah 1. ibid Bikurey Yaakov 2, Teshuvos Binyan Shlomo 43, Sdey Chemed Maareches Succah 2:3. Tosefos Gittin 45b ד”ה כל, Magen Avrohom O:CH 14:3.