Minchah after candle lighting on Shabbat

Q: Is it permissible for a woman to daven Minchah after lighting Shabbat candles?
A: The Mishnah Berurah (263:43) rules that she may not since when she lights the candles she has accepted Shabbat. How then can she daven the weekday Minchah? The majority of halachic authorities, however, say that even though she accepted Shabbat, it is still possible to daven the weekday Minchah. We see in the Mishnah in Shabbat (2:7) that it is permissible to perform certain acts after sundown on Shabbat since we accept "Tosefet Shabbat" (adding to Shabbat) but not Shabbat itself. Others write that one may not daven weekday Minchah after the community accepts Shabbat, but an individual may daven it after accepting Shabbat on his/her own. Therefore even though this appears as "Tartei De-Satrei" (two contradictory acts – lighting Shabbat candles and then davening weekday Minchah), various authorities permit it. See Piskei Teshuvah (Hilchot Shabbat vol. 3, p. 40-41) for the authorities who allow it. This is not only a question for a woman but for a man who arrives at shul late after sundown. It is permissible for him to daven the weekday Minchah.