אורח חיים תקפ״וOrach Chayim 586

Se’if 1א׳

שׁוֹפָר שֶׁל רֹאשׁ הַשָּׁנָה מִצְוָתוֹ בְּשֶׁל אַיִל וְכָפוּף; וּבְדִיעֲבַד, כָּל הַשּׁוֹפָרוֹת כְּשֵׁרִים, בֵּין פְּשׁוּטִים בֵּין כְּפוּפִים, וּמִצְוָה בִּכְפוּפִים יוֹתֵר מִבִּפְשׁוּטִים; וְשֶׁל פָּרָה פָּסוּל בְּכָל גַּוְנָא; וְכֵן קַרְנֵי רֹב הַחַיּוֹת שֶׁהֵם עֶצֶם אֶחָד וְאֵין לָהֶם מִבִּפְנִים זַכְרוּת, פְּסוּלִים. וְכֵן שׁוֹפָר מִבְּהֵמָה טְמֵאָה, פָּסוּל (רַ"ן פ"ג דְּרֹאשׁ הַשָּׁנָה).

The Shofar of Rosh Hashana should be from a ram, bent; under extreme circumstances, all shofars are kosher, whether straight or bent, however the mitzva is better fulfilled with a bent one rather than a straight one; the shofar of a cow may not be used; similarly the horns of most wild animals, as they are a bone and have no hollow inside, may not be used. (Similarly, the shofar of a non-kosher animal may not be used (Ra"n Chapter 3 Rosh Hashana).

Se’if 2ב׳

הַגּוֹזֵל שׁוֹפָר וְתָקַע בּוֹ, יָצָא אֲפִלּוּ לֹא נִתְיָאֲשׁוּ הַבְּעָלִים מִמֶּנּוּ.

2. If one steals a shofar and sounds it, they fulfill their obligation, even if the owners have not given up hope of finding it.

Se’if 3ג׳

תָּקַע בְּשׁוֹפָר שֶׁל עֲבוֹדַת כּוֹכָבִים שֶׁל יִשְׂרָאֵל, לֹא יָצָא. שֶׁאֵינָהּ בְּטֵלָה עוֹלָמִית וְכַתּוּתֵי מִכְתַּת שִׁעוּרֵיהּ; אֲבָל בְּשֶׁל עֲבוֹדַת כּוֹכָבִים שֶׁל עוֹבֵד כּוֹכָבִים, וְכֵן בִּמְשַׁמְּשֵׁי עֲבוֹדַת כּוֹכָבִים שֶׁל עוֹבֵד כּוֹכָבִים, לֹא יִתְקַע; וְאִם תָּקַע בּוֹ, יָצָא וְהוּא שֶׁלֹּא נִתְכַּוֵּן לִזְכּוֹת בּוֹ; אֲבָל אִם נִתְכַּוֵּן לִזְכּוֹת בּוֹ, לֹא יָצָא דַּהֲוָה לֵיהּ עֲבוֹדַת כּוֹכָבִים שֶׁל יִשְׂרָאֵל וְיֵשׁ מַחְמִירִין דַּאֲפִלּוּ בְּשֶׁל עוֹבֵד כּוֹכָבִים אֵינוֹ יוֹצֵא אֶלָּא בְּנִתְבַּטֵּל בְּעֶרֶב יוֹם טוֹב (מָרְדְּכַי) וְעַיֵּן לְעֵיל סי' תרמ"ט (סָעִיף ג').

3. If one blows a shofar that is owned by a Jew and is an object of idol worship, they do not fulfill the mitzvah, as such use for idol worship is never nullified and it is as if the shofar has been crushed to a size too small to use. One should not blow a shofar owned by an idol worshipper that was an object of idol worship or was used in the worship of idols, but if one did blow such a shofar, they have fulfilled their obligation, as long as they did not intend to claim ownership of the shofar [by sounding it]. If one intended to claim ownership of the shofar, they have not fulfilled their obligation, as it is now an object of idol worship owned by a Jew. (There are those who are stringent and who regard even blowing a shofar [that is an object of idol worship] owned by an idol worshipper as fulfilling their obligation unless the shofar's status as an object of idol worship was nullified before the holiday (Mordechai). See 649:3)