Q. If you are walking outside in front of your apartment building on Shabbos and the building has mostly Jews and you see on the ground a wallet, are you allowed to pick it up in order to return it? Do we need to assume that the wallet has cash, credit cards, bank cards that would render the wallet Muksa? Even if we assume that the wallet has cash and is muksa, does the D'oraisa of returning a lost item push off the prohibition of muksa? What if the building is mostly Goyim, would that change the ruling on this?
A. Shulchan Oruch (O.C. 266,13) prohibits picking up an "Arneky" on Shabbes. Biur Halocho (ibid.) forbids retrieval of the Arneky when carrying is an issue (no Eiruv), even if it was found in a place where the majority of residents are Jewish and his intention is to return it to its owner (Hashovas Haaveida). As far as muktza is concerned, he declares that it requires further elucidation and refers us to the O.C. 686,22 and Biur Haggrah ibid. dealing on a Shofar manufactured on Rosh Hashono. Mishnah Berura there (82) explains that if there were an issue of muktza , it would be prohibited to blow the Shofar. There are Poskim who disagree, however, most maintain that even a mitzva of the Torah does not override muktza in this and similar cases. (see: Chasam Sofer O.C. 82, - Divrei Sholom 17 – Mishmeres Sholom Ch. 3, Adonei Shlomo 266 – Shmiras Shabbos 236,28).
Horav Shlomo Miller's Shlit"a opinion is that, the found wallet is muktza and one is forbidden to pick it up, regardless of who the majority of probable owners may be. He suggested, if one is close to the end of Shabbos, to stay with the aveida. (or to kick it to a safe location)
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a