Q: I found an item with a name and phone number in a place that most passersby are gentile. Can I keep it?
A: When you find a lost item after the owner’s yei’ush, which we presume here, halachah allows you to keep it. However, lifnim mishuras hadin — beyond the letter of the law — you should usually return it, based on the verse: “You should inform them ... [what] they should do” (Shemot 18:20) (C.M. 259:5; 259:7; Sma 259:12).
Some write that if the finder is financially sound, beis din should even coerce him verbally to act lifnim mishuras hadin. On the other hand, if the finder is needy and the owner financially sound, Rema writes that the finder does not have to act lifnim mishuras hadin. Some infer that if both are needy, the finder should still return lifnim mishuras hadin (Shach 259:3; Tzemach Tzedek #99; Pischei Teshuvah 12:6, 259:2).
The reason to require acting lifnim mishuras hadin here is because the yei’ush was not of the owner’s free will, unlike full hefker, or because the finder suffers no actual financial loss by returning the item (Shulchan Aruch Harav #18; Aruch Hashulchan 259:7).