Maran in Siman 674 states that "Madlikin Mi’ner L’ner"-It is permitted to light one candle from another candle. For example, one may light the second candle from the flame of the first candle. Since both candles are a Misva, there is no problem. It is even permissible, according to the Sha’ar Ha’siyun (Rav Yisrael Meir Kagan of Radin, 1839-1933), to remove the candle from its place to light the other candle. The Ashkenazim are strict in this matter. However, all agree that one may not light an ordinary candle from the holy Hanukah candles.
The Poskim discuss whether it is permitted to light a mundane candle, such as the Shamush, for the purpose of lighting the candles of Misva. For example, if the Shamush was extinguished while lighting the candles, may it be lit from the already lit Hanukah candles? Maran cites two opinions regarding this issue. The Stam (unattributed opinion) rules that it is prohibited, and the Yesh Omrim (minority opinion) is lenient. The Halacha is in accordance with the Stam that it is prohibited.
If one of the candles was extinguished after burning for only ten minutes, it is prohibited to relight it from one of the other candles. Even though it is permitted to light a Misva candle, in this case, the extinguished candle is no longer considered a Misva, since "Kavta En Zakuk La"-If a Hanukah candle blows out immediately after lighting, the Misva has already been fulfilled and there is no obligation to relight it. Therefore, the extinguished candle is considered a mundane candle.
This restriction only applies to the first half hour after the candles were lit. Afterward, the candles no longer have a status of Misva, and they may be used to light an ordinary candle. Moreover, after the first half hour, it is even permissible to blow out the candles, according to many opinions.
It is permissible to light a Hanukah candle from another Hanukah candle, but it is prohibited to light an ordinary candle from the Hanukah candles, even if the purpose of the ordinary candle is to light other Hanukah candles. Furthermore, it is prohibited to use a Hanukah candle to light another Hanukah candle that was lit but became extinguished immediately afterward. This restriction applies only to the Hanukah candles during their first half hour after being lit.