Siman 667

Even though it was explained in siman 665 that an etrog is permitted on the eighth day in Eretz Yisrael, nevertheless, the sukkah and the decorations of the sukkah are forbidden on the eighth day, for the reason that since they were set aside during the twilight between the seventh and eighth days—they are set aside for the entire day. And it is not similar to an etrog, for the muktzeh is not by means of an action but rather on account of the day that passed. This is not so regarding a sukkah, for behold, one must sit there during twilight. And if a meal happened to occur for him during twilight—he would eat there in the sukkah, and it turns out that its being set aside is by means of an action, as I wrote there. And it follows that in the diaspora, where they also sit on the eighth day, they are also forbidden on the ninth day for this reason; for the ninth day for the inhabitants of the diaspora is like the eighth day for the inhabitants of Eretz Yisrael. And know: that which we said regarding the prohibition to use the sukkah—this is when it fell, for if it is standing—it is anyway forbidden because of demolishing a structure. And if Simchat Torah falls on the eve of Shabbat—some are accustomed to forbid the sukkah and its decorations also on Shabbat, for the reason that if you permit them on Shabbat—behold, the Yom Tov is preparing for Shabbat. However, we have already explained in siman 665 that regarding a thing that already exists in the world—the concept of preparation does not apply. Nevertheless, there are those who are stringent, as I wrote there, see there.

There are those who were accustomed, when they would exit the sukkah, to say: "May it be Your will... just as we have merited to sit in this sukkah, so may we merit to sit in the sukkah of the skin of the Leviathan." And it is a known matter that it is forbidden to prepare from one Yom Tov for the next; therefore, on Shemini Atzeret, when they bring down the vessels from the sukkah, it is forbidden to set up the tables and the benches in the house for the needs of the night, as this constitutes preparation. It is sufficient that we permitted bringing them down from the sukkah during the day because it is impossible at night. But to set them up and arrange them is forbidden until the night. This is when the bringing down is a matter unto itself, and the arranging is a matter unto itself. But if at the time of bringing them down one sets them in their place, we have no concern with it, for there is no specific action or exertion unto itself in this. (And with this is answered what was difficult for the Magen Avraham in subsection 3 from the words of the Maharil, see there. For the Maharil forbids searching for the Sefer Torah from Shabbat for Yom Tov because of preparation, see there. It seems to me that if one says there some verses of the Torah, it is like learning for that moment, and it is not called preparation.)