Qitzur Shulchan Arukh – 187:1-2
סִימָן קפז – הִלְכוֹת אֲבֵדָה וּמְצִיאָה
186: Laws of Lost and Found Items
Someone who sees something lost by a Jew, he is obligated to busy himself with it to return it to its owner, as it says, “[Do not see your brother’s ox or his sheep driven away, and you hide yourself from them;] you must bring them back [to your brother].” (Devarim 22:1) Similarly, any of his friend’s money that a person can save from getting lost, he is obligated to save, and it is within the category of “returning lost items”.
Even though by the strict law, in a place where most of [the people] are non-Jews, even if a Jew put on his item a sign [the finder] isn’t obligated to return it — because the usual situation would be that [the one who lost it] gave up on it [being returned] — in any case it is good and right to go within the line of the law to return to a Jew who put a sign on the item. And we compel someone to do so. If the finder is a poor person, and the one who lost it is wealthy, he isn’t requires to go beyond the letter of the law.
In a place where there is a civil aw requiring the return of lost items, he is obligated in any situation to return it [– Jew or non-Jew, sign or no sign].
As you may have noticed from previous comments, e.g. about charging interest (65:1), my rule of thumb is that if the action is not obligatory/prohibited where the other party is a Jew then the issue isn’t one of monetary fairness, but of brotherhood.
I therefore would conclude from here that — barring local law — “finder’s keepers losers weepers” is a valid fiscal principle. However, when local law is that a person retains ownership of a lost item, then a Jew would be obligated to return the item for two reasons:
1: Local custom can define fiscal norms, and therefore the law means the non-Jew still owns the item. To use it would be theft.
2: There is a halachic obligation to be a law abiding citizen (assuming the law neither calls for a violation of halakhah nor is anti-semitic in intent).
yes i remeber we focused on this question at dati school and this law also says that if you cant find the owner of the lost item you have rights for it and it can become yours))