I hope you enjoy the following timely repeat of an earlier post. Best wishes for a gut yom tov.
The Shaarei Teshuvah (589:3) cites the Shagas Aryeh (siman 106) who maintains that one is not allowed to carry a shofar or a lulav into a reshus harabbim (where there is no eruv) for a woman or a child since they are not required to partake in this mitzvah. The Shagas Aryeh (siman 108) adds that once one has fulfilled his obligation min haTorah of shofar or lulav he cannot carry them into a reshus harabbim to fulfill a mitzvah d’rabbanan (e.g. once one has fulfilled tekiyos d’meyushav he would not be permitted to carry the shofer for tekiyos d’mussaf or, as some have a minhag to shake the lulav in the sukkah in the morning, they would not be allowed to carry it to shul afterwards for the na’anuim during Hallel).
However, most poskim disagree and allow the carrying of a shofar or a lulav for a woman or a child as well as to fulfill a mitzvah d’rabbanan (Shiurei Bracha, 589:2; Yosef Omets, siman 82; Shulchan Aruch HaRav, 589:2; Orchos Chaim, 589:3; Daas Torah, 589; Kaf HaChaim, 589:28, regarding a woman; Ketzeh HaMateh, 389:5; Igros Moshe, O.C. 3:94, see also Part 2a: Why Brooklyn Is Not a Reshus HaRabbim; Oz Nidberu, 13:38).
The Elef HaMagen (660:1; see also Ketzeh HaMateh, 389:5, and Kuntres Achron) cites the Ostrovtzer rav that the Shagas Aryeh is referring only to a situation of a reshus harabbim d’Oraysa. However, since we do not have a reshus harabbim d’Oraysa today (because we rely on the criterion of shishim ribo) the Shagas Aryeh’s issues do not concern us.
[The Teshuvos V’Hanhagos (1:348) states that after one has fulfilled all his d’Oraysa and d’rabbanan obligations of shaking the lulav (in an area without an eruv), and there is no concern of shmira, the lulav cannot be carried anymore (there can also be an issue of hachanah, preparation for another day). However, the Sheraga HaMe’ir (5:72) maintains that if one preserves the lulav in water, he may carry it home because the lulav has to be returned to the same water it was in originally (see Shulchan Aruch, O.C. 654).]