Siman 681
Presented here for study, not as a practical ruling. The Shulchan Aruch rules by Sephardi custom, the Rema's glosses by Ashkenazi custom, and the Kitzur follows Ashkenazi custom. For a practical question, ask your rabbi.
א בְּמוֹצָאֵי שַׁבָּת אֵין מַבְדִּילִין בְּנֵר חֲנֻכָּה, שֶׁאֵין נֶהֱנִים לְאוֹרוֹ וְאֵין מְבָרְכִין עַל הַנֵּר עַד שֶׁיֵּאוֹתוּ לְאוֹרוֹ.
1 We Do Not Perform the Havdalah With the Hanukkah Light After the Sabbath, 2 Seifim: After the Sabbath we do not perform the havdalah with the Hanukkah light, for we may not derive pleasure from its illumination, and we do not recite the benediction over the [havdalah] light until we bask in its illumination.
ב מַדְלִיקִין נֵר חֲנֻכָּה בְּבֵית הַכְּנֶסֶת קֹדֶם הַהַבְדָּלָה. הַגָּה: וְכָל שֶׁכֵּן בְּבֵיתוֹ שֶׁמַּדְלִיק וְאַחַר כָּךְ מַבְדִּיל, שֶׁהֲרֵי כְּבָר הִבְדִּיל בְּבֵית הַכְּנֶסֶת.
2 We kindle the Hanukkah light in the synagogue before the havdalah. Rema: And all the more so at home where one kindles and afterward performs the havdalah, for havdalah has already been performed in the synagogue.