The Talmud articulates the principle of 'shome'a k'oneh' — that hearing a blessing recited by another is equivalent to reciting it oneself — the core principle at stake in determining whether Havdalah over the telephone can work.
הוּא אוֹמֵר: ״אָנָא ה׳ הַצְלִיחָה נָּא״ וְהֵן אוֹמְרִים: ״אָנָּא ה׳ הַצְלִיחָה נָּא״, מִכָּאן שֶׁאִם בָּא לִכְפּוֹל — כּוֹפֵל. הוּא אוֹמֵר: ״בָּרוּךְ הַבָּא״, וְהֵן אוֹמְרִים: ״בְּשֵׁם ה׳״ — מִכָּאן לְשׁוֹמֵעַ כְּעוֹנֶה. בְּעוֹ מִינֵּיהּ מֵרַבִּי חִיָּיא בַּר אַבָּא: שָׁמַע וְלֹא עָנָה, מַהוּ? אֲמַר לְהוּ: חַכִּימַיָּא וְסָפְרַיָּא וְרֵישֵׁי עַמָּא וְדָרָשַׁיָּא אָמְרוּ: שָׁמַע וְלֹא עָנָה — יָצָא. אִתְּמַר נָמֵי, אָמַר רַבִּי שִׁמְעוֹן בֶּן פַּזִּי אָמַר רַבִּי יְהוֹשֻׁעַ בֶּן לֵוִי מִשּׁוּם בַּר קַפָּרָא: מִנַּיִן לְשׁוֹמֵעַ כְּעוֹנֶה — דִּכְתִיב: ״אֶת (הַדְּבָרִים) אֲשֶׁר קָרָא (יֹאשִׁיָּהוּ)״. וְכִי יֹאשִׁיָּהוּ קְרָאָן? וַהֲלֹא שָׁפָן קְרָאָן, דִּכְתִיב: ״וַיִּקְרָאֵהוּ שָׁפָן (אֵת כׇּל הַדְּבָרִים הָאֵלֶּה) לִפְנֵי הַמֶּלֶךְ״. אֶלָּא, מִכָּאן לְשׁוֹמֵעַ כְּעוֹנֶה.
The prayer leader recites: “Lord, please grant us success,” and the congregation recites in response: “Lord, please grant us success” (Psalms 118:25). From here is the source of the halakha that if one comes to repeat a particular verse in hallel twice, he may repeat it. The prayer leader recites: “Blessed is one who comes” (Psalms 118:26), and the congregation recites the rest of the verse: “In the name of the Lord” (Psalms 118:26), in response. From here is the source of the halakha that the halakhic status of one who hears a passage recited is equivalent to that of one who recites it, as the congregation fulfills its obligation even though it does not repeat the entire verse. Apropos this halakha, the Gemara relates that the Sages raised a dilemma before Rabbi Ḥiyya bar Abba: If one heard a passage recited and did not recite it himself, what is the halakha? Did he fulfill his obligation or not? He said to them that the Sages, and the schoolteachers, and the heads of the nation, and the homiletic interpreters said: One who heard a passage recited and did not recite it himself fulfilled his obligation. It was also stated that Rabbi Shimon ben Pazi said that Rabbi Yehoshua ben Levi said in the name of Bar Kappara: From where is it derived that the halakhic status of one who hears a passage recited is equivalent to that of one who recites it? It is as it is written: “All the words of the book which the king of Judea has read” (II Kings 22:16). And did King Josiah read them? Didn’t Shaphan read them, as it is written: “And Shaphan read it before the king” (II Kings 22:10)? Rather, from here it is derived that the halakhic status of one who hears a passage recited is equivalent to that of one who recites it, and it is as though Josiah read the words himself.