On Erev Shabbos, if a woman is running late to light Shabbos candles on time, she is permitted to light the Shabbos candles immediately, once her husband has lit even one of the lights on the Chanukah menorah, and she will be yotzeh with her husband’s lighting.
(Rama end of 671:7, Halichos Yosef 679:1, Ben Ish Chai 1:Vayeishev:Chanukah:20)
The Mishnah Brurah brings in the name of the Pri Migadim and Shaarei Teshuva that on Erev Shabbos, lechatchila, one should daven Minchah before lighting Chanukah licht (if possible). Nevertheless, most communities are not makpid on this and daven after lighting.
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