Qitzur Shulchan Arukh – 187:3-5

ג: כָּל הַמּוֹצֵא אֲבֵדָה, בֵּין שֶׁיֵשׁ בָּהּ סִימָן בֵּין שֶׁאֵין בָּהּ סִימָן, אִם מְצָאָהּ דֶּרֶךְ הַנָּחָה, כְּגוֹן טַלִּית וְקַרְדֹּם בְּצַד הַגָּדֵר, וַאֲפִלּוּ יֵשׁ לְהִסְתַּפֵּק אִם הִנִּיחָם שָׁם בְּכַוָּנָה אוֹ אִבְּדָם ֹשָם, אָסוּר לִגַּע בָּהֶם

Anyone who finds a lost item,whether it has an [identifying] sign or whether it has no sign, if he found it in a manner in which it is usually placed down, like a tallis or axe alongside a fence, Even if there is reason to be unsure whether he placed them their intentionally or left them there, it is prohibited to touch them.

ד:מִי שֶׁהוּא זָקֵן מְכֻבָּד, וּמָצָא אֲבֵדָה וְהוּא דָבָר מְבֻזֶּה, שֶׁאֲפִלּוּ הָיָה שֶׁלּוֹ, לֹא הָיָה נוֹטְלוֹ לַהֲבִיאוֹ לְבֵיתוֹ, מִשּׁוּם דַהֲוֵי לֵהּ בִּזָּיוֹן, אֵינוֹ חַיָב לְטַּפֵּל בָּהּ. וּמִכָּל מָקוֹם יֶשׁ לוֹ לַעֲשׂוֹת לִפְנִים מִשּׁוּרַת הַדִין וּלְטַפֵּל בָּהּ, אַף-עַל-פִּי שֶׁאֵינָהּ לְפִי כְבוֹדוֹ

Someone who is a respected elder and he finds a lost item which is embarrassing, so that even if it were his he wouldn’t pick it up to bring it to his home because is would be embarrassing for him, he doesn’t have to busy himself with it. In any case, it is appropriate for him to act within the limit of the law and busy himself with [returning] it, even though it is not according to his honor.

ה:מָצָא מְצִיאָה וְאֵינוֹ יוֹדֵע מִי אִבְּדָהּ, בֵּין שֶׁיֵשׁ בָּה סִימָן בֵּין ֹשֶאֵין בָּהּ סִימָן, יֵשׁ בְּעִנְיָנִים אֵלּוּ הַרְבֵּה חִלּוּקֵי דִינִים, וְיַעֲשֶׂה שְׁאֵלַת חָכָם אֵיךְ יַעֲשֶׂה

Someone who finds something and does not know who lost it, whether it has a sign or whether it doesn’t have a sign, there are in these topics many distinctions between the laws, and you should ask a learned person what to do.

A lesson to take even from se’if 5’s statement that the laws are too involved for a brief guide like the Qitzur Shulchan Arukh. How much quicker we are to ask a rabbi a question of kashrus than one of proper financial behavior! Notice the warning here; these laws too have their complexities, and cultivating a habit of consulting one’s rabbi when they touch issues that are beyond our knowledge is appropriate.

Qitzur Shulchan Arukh – 187:1-2

סִימָן קפז – הִלְכוֹת אֲבֵדָה וּמְצִיאָה

186: Laws of Lost and Found Items

א: הָרוֹאֶה אֲבֵדַת יִשְׂרָאֵל, חַיָב לִטַּפֵּל בָּהּ לַהֲשִׁיבָהּ לִבְעָלֶיהָ, שֶׁנֶּאֱמַר, “הָשֵׁ֥ב תְּשִׁיבֵ֖ם”. וְכֵן כָּל מָמוֹן שֶׁל חֲבֵרוֹ שֶׁאָדָם יָכוֹל לְהַצִּיל ֹשֶלֹּא יֹּאבַד, חַיָב לְהַצִּיל, וְהוּא בִּכְלַל הֲשָׁבַת אֲבֵדָה

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”.

ב: אַף-עַל-פִּי שֶׁמִּן הַדִין בְּמָקוֹם שֶׁרֹב גּוֹיִם מְצוּיִים, אֲפִלוּ נָתַן בָּהּ יִשְׂרָאֵל סִימָן, אֵינוֹ חַיָב לְהַחֲזִיר, מִשּׁוּם דְמִסְּתָמָא כְּבָר נִתְיָאֵשׁ הֵימֶנָּה, מִכָּל מָקוֹם טוֹב וְיָשָׁר לַעֲשׂוֹת לִפְנִים מִשּׁוּרַת הַדִּין לְהַחֲזִיר לְיִשְׂרָאֵל שֶׁנָּתַן בָּהּ סִימָן. וְכוֹפִין עַל זֶה. וְאִם הַמּוֹצֵא הוּא עָנִי, וּבַעַל הָאֲבֵדָה הוּא עָשִׁיר, אֵינוֹ צָרִיךְ לַעֲשׂוֹת לִפְנִים מִשּׁוּרַת הַדִין. וּבְמָקוֹם שֶׁיֵשׁ דִּינָא דְמַלְכוּתָא לְהַחֲזִיר אֲבֵדָה, חַיָב בְּכָל עִנְיָן לְהַחֲזִיר

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).