Davening Mincha after candle lighting on Erev Shabbos:[1]

A woman who lights Shabbos candles, and thus accepts Shabbos with her lighting, is to Daven Mincha beforehand.[2] [If she did not do so, and has already lit her candles, then she may not daven Mincha afterwards, and is to rather Daven Maariv twice.[3] However, some Poskim[4] are lenient and rule that Bedieved she may still Daven Mincha after lighting candles and accepting Shabbos, especially if she had in mind to do so before the lighting.[5] Practically, initially, if she sees that she will not have time to Daven Mincha before lighting candles, she is to stipulate that she does not plan to accept Shabbos with her lighting.[6] In such a case she may light the candles, and then Daven Mincha, and then accept Shabbos, although the accepting of Shabbos must be done within ten minutes from the lighting.[7] If she did not make this stipulation and already lit candles, she is to daven Maariv twice, although those who nevertheless Daven Mincha have upon whom to rely. If a man is lighting candles, he may always delay accepting Shabbos and daven Mincha after the lighting[8], so long as he [Davens Mincha and] accepts Shabbos within ten minutes from the lighting.[9] However, some are accustomed to Daven Mincha before lighting even regarding men.[10]]

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[1] Admur 263:7; M”A 263:19 in name of Masas Binyamon; Elya Raba 263:17; Machatzis Hashekel ibid, P”M 263 A”A 19; Mishneh Berurah 263:43; Ketzos Hashulchan 74:5; See Piskeiy Teshuvos 263:41; Kitzur Dinei Hadlakas Neiros 2:15

[2] The reason: As once a woman lights candles, she accepts Shabbos with that lighting, and one cannot Daven Mincha of Friday when they have just accepted that it is no longer Friday, but Shabbos. [Machatzis Hashekel on M”A ibid, based on Michaber 263:15; P”M 263 A”A 19; Mishneh Berurah 263:43;] If however one did not light candles, and did not accept the essence of Shabbos, then even if he accepted Tosefes Shabbos, he may still Daven Mincha. The reason for this is because when a woman lights candles she accepts the essence of Shabbos [Itzumo Shel Yom], as opposed to Tosefes Shabbos. [Ketzos Hashulchan 76 footnote 1; See Admur Seder Hachnasas Shabbos who allows Davening Mincha even after sunset; Mishmeres Shalom 26/23; See Admur 393:2 regarding the difference between accepting Tosefes Shabbos and Itzumo Shel Yom]

[3] Machatzis Hashekel 263 ibid as rules Michaber 263:15 regarding one who said Barchu; M”B 263:43; Kaf Hachaim 263:65; Ketzos Hashulchan 74:5

[4] Ashel Avraham Butchach 263 says to make Tnaiy regarding Mincha alone [and may accept Shabbos]; Orchos Chaim 261:1; 263:12; Lev Chaim 3:57; Eretz Tzevi 1:60 [permits even without Tnaiy]; Minchas Yitzchak 9:20 [permits without Tnaiy as rules Eretz Tzevi]; See Divrei Yatziv 1:121; Beir Moshe 1:15; Az Nidbaru 2:2; Rivivos Efraim 4:69; Piskiey Teshuvos 253:41 concludes that those who are lenient have upon whom to rely

[5] The reason: As the ruling of the M”A ibid was only regarding Lechtachila and not Bedieved. [Eretz Tzevi ibid; Minchas Yitzchak ibid] Likewise, perhaps, lighting candles is not considered as if one is accepting Itzumo Shel Yom, but rather Tosefes Shabbos. [So rules Chasam Sofer 65] Some suggest that perhaps the acceptance of Shabbos opposes Mincha only when done with the public, such as when answering Borchu and the like, and not by a private acceptance.

[6] Ashel Avraham Butchach 263 says to make Tnaiy regarding Mincha alone [and may accept Shabbos]; Ben Ish Chaiy Noach 9; Kaf Hachaim 263:35; Beir Moshe 1:15; 8:64; Even Yisrael 8:21; Minchas Shlomo 2:35; SSH”K 43 footnote 128; Kinyan Torah 2; Teshuvos Vehanhagos 4:62; Piskeiy Teshuvos 263:41; Admur ibid permits making a stipulation in a time of need

Other opinions: Some Poskim imply that she is not to make a stipulation, but is rather to Daven Maariv twice. [See M”B ibid; Piskeiy Teshuvos 263 footnote 387]

[7] See Admur 263:6, 7, 11 that she must accept Shabbos immediately after the lighting and Kuntrus Achron 263:2 that this is within much less than 14 minutes; Ketzos Hashulchan 74 footnote 17 that this is within 10 minutes; Piskeiy Teshuvos 263:15 and 32 writes ten minutes

Other opinions: Some Poskim rule it is not necessary to accept Shabbos immediately after candle lighting, after the time of Plag Hamincha. [Rav Akiva Eiger263; M”B 263:20; Biur Halacha 263:4 “Mibiod Yom”; Eretz Tzevi 113]

[8] See Admur 263:7 that a man does not accept Itzumo Shel Yom with his lighting; Piskeiy Teshuvos 263:41; There were times that the Rebbe lit Chanukah candles, and then Shabbos candles and only then Davened Mincha with the Minyan. [Hiskashrus 908 footnote 77]

[9] See Poskim in previous footnotes

[10] Mishmeres Shalom Kudinov 26/23