Shulchan Aruch Chapter 674:
It is Permitted to Light From Candle To Candle (2 Paragraphs)
REMA in Brackets [ ]

1.  One is permitted to light the Chanukah candles from one candle to another.  This applies if one uses one candle directly to another without any other candle in between them.  But to take fire from one Chanukah candle using a regular candle and to light another Chanukah candle with it is forbidden.  However, there are those who permit this unless there is a concern that the regular candle will go out before the other Chanukah candle is lit.  [Our custom is to be stringent with the Chanukah candles and to not light even from one Chanukah candle to another.  The reason is that the main Mitzvah (positive commandment) is to light only one candle and the rest are not really a Mitzvah.  This is only applicable when the lit candles are actively performing the Mitzvah.  But after the time of the Mitzvah passed, then it is permitted to derive benefit from them and surely it is permitted to light with them.

2.  There are those who claim that the candles of the Synagogue, the candles of Shabbat, and the candles of Chanukah are all a Mitzvah.  According to this opinion it is permitted to light any of these three from one of them.  [The same applies to the candles of  ת'ת 1 and the candle lit for a sick person who needs a light.  With regard to the candles of the synagogue, see Ch 154 p14. ]
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Shulchan Aruch Chapter 675:
That The Lighting is the Mitzvah and Not the Placing (3 Paragraphs)

1.  The act of lighting is the Mitzvah and not the placing.  So if it was placed in a certain spot without the intention of Chanukah and then lit over there, one need not remove it and reposition it for the Mitzvah of Chanukah.  Therefore if one had candles that were lit the entire day starting from the eve of Shabbat where they were lit for the Mitzvah of Chanukah and they were still burning after the Shabbat, one may extinguish them and relight them for the Mitzvah of Chanukah.  However, it is necessary that one lights them where they are set in (the proper) place.  For if one lights them indoors and then takes them outside, one does not fulfill his obligation since one who sees this will say that he lit them for his own benefit.  Similarly, if one lit the candles and then took hold of them in his hand at its current location, he does not fulfill his obligation because one who sees this will say that he grabbed it for his own benefit. 

2.  There are those who say that since the act of lighting is the Mitzvah, it is necessary to put enough oil in the lamp before lighting it to fulfill the minimum requirement.  But if he lit it and then added enough oil, he does not fulfill his obligation. 

3.  A woman may light the Chanukah candles since she is also obligated in it.  But if a blind person, a fool, or a minor lit them it does not count as anything even if an adult did the placing.  There are those who say that if a child reached the age of teaching then it is permitted for him to light the Menorah.  [By us where every member of the home lights, a minor that reached the age of teaching must also light.]
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