The Shulchan Aruch · Orach Chayim
אורח חיים ט״וOrach Chayim 15
Siman 15 of 697 in Orach Chayim — 6 se'ifim
הלכות ציציתLaws of Tzitzit· siman 15
Se’if 1א׳
מֻתָּר לְהַתִּיר צִיצִיּוֹת מִטַּלִּית זֶה וְלִתְּנָם בְּטַלִּית אַחֵר אֲבָל שֶׁלֹּא לְהַנִּיחָם בְּבֶגֶד אַחֵר לֹא: הַגָּה: וְדַוְקָא בְּטַלִּית שֶׁל בַּר חִיּוּבָא אֲבָל מֻתָּר לְהַתִּיר צִיצִית מִטַּלִּית שֶׁל מֵתִים (מָרְדְּכַי וְתוס' פֶּרֶק ב"מ דַּף כ"ב).
If One Is Allowed To Untie ציצית From One Garment [And Transfer It] To Another, and The Laws Of [What To Do If] One's טלית Ripped, Containing 6 Se'ifim One is allowed to untie ציצית from one טלית and to place them on another טלית; however, [to untie them] without placing them on another garment, that is not allowed. Rem"a: And this [prohibition of untying ציצית] applies specifically to a טלית [that belongs to] one who is obligated [to wear it], but it is permitted to untie the ציצית from a טלית of a dead person [without needing to place them on another garment.] (See Mordechi and Tosafot Shabbat 22a).
Se’if 2ב׳
אֵינוֹ יָכוֹל לִקַּח הַכָּנָף כְּמוֹ שֶׁהוּא עִם הַצִּיצִית וּלְתָפְרוֹ בְּבֶגֶד אַחֵר מִשּׁוּם דְּעַל כַּנְפֵי בִגְדֵיהֶם בָּעֵינָן וְכָנָף זֶה לֹא הָיָה מִבֶּגֶד זֶה בִּשְׁעַת עֲשִׂיָּה.
One may not take the [detached] corner [of a garment] as it is, with the ציצית [still attached], and to sew it onto another garment, because it needs to be "...on the corner of their garments..." (Numbers 15:38), and this corner [that is being sewed on] was not part of this garment [that it's being sewed on to] when it was made.
Se’if 3ג׳
טַלִּית מְצֻיֶּצֶת כְּהִלְכָתָהּ שֶׁחִלְּקוּהָ לִשְׁתַּיִם וּבְכָל חֵלֶק יֵשׁ בּוֹ כְּשִׁעוּר לְהִתְעַטֵּף, וְנִשְׁאַר לְכָל אַחַת מֵהֶם צִיצִית אַחַת אוֹ שְׁתַּיִם, אֵין בּוֹ מִשּׁוּם תַּעֲשֶׂה וְלֹא מִן הֶעָשׂוּי.
A טלית that had ציצית on it in accordance with the law, that was split into two, and each part has [at least] the [minimum] measurement [of garment] to wrap oneself with it (ie. it's large enough to be obligated in ציצית), and there remained, on each one of the parts, ציצית on 1 or 2 [of the corners], there is no concern for [the invalidation of] "You shall make it, and not from that which is [already] made".
Shulchan Aruch, Orach Chayim — Torat Emet 363 edition, via Sefaria — public domain
English: Sefaria Community Translation — CC0