The Chatam Sofer, in one of his responsa (O.C. 184; cited in Bei’ur Halakha to 638:2), addresses the case of somebody who had hung an etrog in his sukka for decoration, and then during Sukkot he wanted to give it to somebody who had been unable to obtain an etrog for the mitzva of arba minim. The Shulchan Arukh (O.C. 638:2) rules that items hung in the sukka for decoration are forbidden for personal use during Sukkot, and the question thus becomes whether using a decoration for a mitzva purpose – such as the mitzva of arba minim – is included in this prohibition.
The Chatam Sofer ruled that this is permissible, for two reasons. First, he notes the famous principle of “mitzvot lav lei-hanot nitenu,” which means that performing a mitzva does not qualify as halakhic “hana’a” (“enjoyment,” or “benefit”). Something forbidden for personal use is not forbidden for mitzva use, and so an etrog hung as a decoration in the sukka may be used for a mitzva purpose. Secondly, the Chatam Sofer writes that the basis of the prohibition against using sukka decorations is bizui mitzva – the disrespect shown to the decorations, which were designated for the mitzva of enhancing the sukka. Using a mitzva object for another mitzva is not halakhically regarded as disrespect, the Chatam Sofer observes, as evidenced by the fact that one may remove tzitzit strings from a garment to affix them onto another garment, and one may light a Chanukah candle from a different candle. Similarly, then, it would be permissible to take an etrog that had been used for decorating a sukka and use it for the mitzva of arba minim.
Rav Eliezer Waldenberg, in his Tzitz Eliezer (13:67), applies the Chatam Sofer’s ruling to permit taking a decoration from one sukka and hanging it in another. This issue could arise in the case of a young child who prepared a decoration in school which was hung in the child’s family’s sukka, and during Sukkot the family visits the child’s grandparents. Rav Waldenberg rules that the family would be allowed to remove the decoration from the sukka (during Chol Ha’mo’ed) in order for it to then be hung in the grandparents’ sukka. Since the decoration is being used for a different mitzva purpose, this is permissible.
However, Rav Moshe Sternbuch, in his Moadim U-zmanim (6:68), makes an exception to this halakha, ruling that it is forbidden to take a decoration hanging from the sekhakh of a sukka and move it to the wall. The Rama (638:2) writes that the status of decorations hung from the wall is questionable, given the view of the Rosh that even the sukka walls themselves are permissible for personal benefit on Sukkot. In light of this uncertainty, the Rama rules that there is greater room for leniency when it comes to the wall decorations, which are not regarded as muktzeh on Shabbat and Yom Tov the way the sekhakh decorations are. As such, Rav Sternbuch writes that one should not move decorations hung from the sekhakh to the wall, since this might constitute a reduction of their status. Since decorations on the wall might not be infused with the halakhic sanctity assigned to the decorations hung from the sekhakh, it would be forbidden, at least according to Rav Sternbuch, to move a decoration from the sekhakh to the wall.