Shulchan Arukh Orach Chayim · Siman 674

English

That it is Permitted to Kindle Lights From One Another, 2 Seifim: We kindle one Hanukkah light from [another] Hanukkah light, and specifically kindling one from another without an intermediary, but kindling one from another through a non-sacred light is prohibited. And some permit even this, unless it is in such a way that there is concern that the non-sacred light will be extinguished before kindling the other Hanukkah light. RAMA: And we have adopted the custom to be stringent with the Hanukkah lights not to kindle even from one light to another, for its main mitzvah is only one candle, and the rest are not as much for the mitzvah. Therefore one should not kindle one from another. (Hagahot Maimoniot and Mordechai) And all this is only while they are still alight for the mitzvah, but after the time of the mitzvah has passed, it is permitted to benefit from them, [so] all the more so it is permitted to kindle from them. (Beis Yosef)

English

There is an [opinion] that says that the lights of the synagogue, of the Sabbath, and of Hanukkah are all mitzvah [lights] and it is permitted to light one from another. RAMA: It is the same law for a light for Torah study or a light for a sick person who needs a light, (Nimukei Yosef) (and regarding the light of the synagogue see above 154:14).