Davening Mincha past sunset:
The prayer of Mincha may be recited until evening. It is disputed amongst Poskim as to the definition of “evening.” Some Poskim rule it is permitted [even initially] to Daven Mincha past sunset, up until Tzeis Hakochavim. Other Poskim rule one may not Daven Mincha past sunset. Practically, one is to initially Daven Mincha before sunset, although one is not to protest against those who are lenient to Daven Mincha after sunset, until Tzeis Hakochavim. This applies both on Shabbos and during the week. This especially applies, in a time of need, such as in the short winter days, [that one may be lenient to Daven Mincha after sunset, up until nightfall].
Initially, one is to Daven Mincha before sunset, although one is not to protest against those who are lenient to Daven Mincha after sunset, until Tzeis Hakochavim. This applies both on Shabbos and during the week. In a time of need, such as in the short winter days, one may be lenient to Daven Mincha after sunset, up until nightfall.
Is it better to Daven Mincha in private before sunset than to Daven with a Minyan after sunset?
Some Poskim it is better to Daven Mincha in private before sunset than with a Minyan after sunset. Other Poskim however rule it is better to Daven Mincha with a Minyan after sunset, then to Daven in private beforehand. It is unclear from Admur as to what his opinion is on the matter.
Is one to initially Daven Mincha with enough time to complete Shemoneh Esrei before sunset?
May one Daven Mincha past Tzeis Hakochavim?
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 See Piskeiy Teshuvos 233:6; Biurim on Seder Hachnasas Shabbbos [Levin] p. 65-67; Halacha Berura [Rav Dovid Yosef] 233
 Chachamim in Mishneh Brachos 26a and Michaber 233:1, based on Talmidei Rabbeinu Yona on Rif Brachos ibid, that the custom is like Chachamim; See also Shut Admur 7 “And in these generations, many are stringent to Daven Maariv on time”; See Tzemach Tzedek Chidushin on Brachos ibid
Opinion of Rebbe Yehuda: Rebbe Yehuda in the Mishneh ibid famously ruled that Mincha may only be prayed until Plag Hamincha. Thus, the question of Davening Mincha past sunset is only relevant to the opinion of the Chachamim. Practically, the Michaber concludes that the custom is like Chachamim and so is the widespread custom today.
 Implication of Michaber ibid “Until nighttime according to Chachamim..And now that the custom is to Daven Mincha until nighttime” [so implies Aruch Hashulchan 233:8 and M”B 233:14, unlike his interpretation in 233:8]; Rama ibid “He is Yotzei if he Davens Mincha until nighttime, which is until Tzeis Hakochavim”; Shaagas Aryeh 17; P”M 89 M”Z 1 “Bein Hashmashos is also a time of Mincha for Chachamim”; 106 M”Z end of siman “Mincha can also be prayed during Bein Hashmashos” [contradicts P”M 233 A”A 7] Implication of Gr”a 233 [unlike Gr”a 261, see Shaar Hatziyon 233:18]; Ashel Avraham of Butchach 233 “The time of Mincha is until Tzeis Hakochavim”; Maharam Shick 91; Rav Poalim 2:19 based on Poskim and Mekubalim and that so is custom in in Yerushalayim and Chevron; and Ben Ish Chaiy Vayakhel 7 regarding women; Kaf Hachaim 233:4-5; Eretz Tzevi 1:1; Shut Beis Avi that so is custom of Polish Jewry to even initially Daven Mincha past sunset; Minchas Elazar 1:13 and Nimukei Orach Chaim 131:2 that the custom of the Belzer Rav was to delay Mincha until close to Tzeis Hakochavim; Meumei Sadeh on Brachos ibid [of Nesiv]; Divrei Yatziv 98-99 that so was custom of Tzanzer Rebbe, Chasam Sofer and Reb Akiva Eiger and so is agreed to by more than 40 Rishonim and Achronim; See Aruch Hashulchan 233:8; Or Letziyon 1:20; Yechaveh Daas 5:22; Mishneh Halachos 7:32; Halacha Berura [Rav Dovid Yosef] 233 for list of many Rishonim and Achronim
 So is implied from wording of Poskim ibid, and so is explicitly written in some Poskim ibid; Now, although the Rama permits only Bedieved and time of need, this is because he was referring to those who follow Rebbe Yehuda on a normal basis, however for those who always follow Chachamim, he too would agree that even initially it is allowed
 The reason: Perhaps the reason is because Mincha is Rabbinical, and the Sages permitted reciting it during Bein Hashmashos, due to Safek Derabanon Lihakel. [Aruch Hashulchan ibid; see Admur in Seder Hachnasas Shabbos] Alternatively, the reason is because Mincha corresponds to the Ketores and not to the afternoon Tamid, and the Ketores was allowed to be offered until Tzeis Hakochavim. [Hagahos Maimanis Tefila 3:3 in name of Rabbeinu Chananel; Aruch Hashulchan ibid; See Biur Hagr”a ibid] Alternatively, in truth the limbs of the afternoon Tamid could be offered until Tzeis Hakochavim. [Pnei Yehoshua Brachos 27a; Shaagas Aryeh ibid] The Talmidei Habaal Shem Tov would intentionally delay Mincha until close to night in order to battel the Kelipos of darkness with their prayers. [Nimukei Orach Chaim ibid]
 Rambam Tefila 3:4; Talmidei Rabbeinu Yona on Rif Brachos ibid “Do not interpret evening to mean until nightfall but rather until sunset”; Shiltei Hagiborim on Mordechai; Kneses Hagedola 233; Lechem Chamudos; Levush 233; Gr”a 261 and in Maaseh Rav 64 [unlike Gr”a 233, see Shaar Hatziyon 233:18]; P”M 233 A”A 7 “Until Tzeis Hakochavim is difficult to allow” [contradicts P”M 89 M”Z 1; 106 M”Z end of siman]; Aruch Hashulchan ibid concludes to be stringent like Rambam and not Daven Mincha after sunset and to protest strongly against those who do; M”B 233:7 and 14 interprets Michaber and Rama ibid “until night” and “until Tzeis Hakochavim” to mean “until the beginning of Bein Hashmashos” however he then writes that the simple implication is until Tzeis Hakochavim. The M”B ibid concludes to be stringent like the above Poskim to be very careful to Daven Mincha before sunset and that only Bedieved and in a great time of need may one be lenient, and even then only until 15 minutes before Tzeis Hakochavim; See Halacha Berura [Rav Dovid Yosef] 233 for list of many Rishonim and Achronim
Does the above opinion follow the opinion of Geonim or Rabbeinu Tam? See M”B ibid who is clearly going on the opinion of Rabbeinu Tam, and so can be interpreted in many of the above Poskim. See Piskeiy Teshuvos 233:8
 The reason: As the prayer of Mincha was instituted in correspondence to the afternoon Tamid sacrifice, whose blood could only be offered until sunset. [Talmidei Rabbeinu Yona on Rif ibid]
 Admur in Seder Hachnasas Shabbbos “However regarding Mincha, which is Rabbinical, one is not to protest against those who are lenient whether during the week or on Shabbos, especially in a time of need during the short winter days.”; Ketzos Hashulchan 26:1 “Mincha may be prayed until sunset, although Bedieved one is Yotzei until Tzeis Hakochavim”; All Poskim brought in coming footnotes who say in time of need may Daven after sunset
 Admur ibid
 Poskim in next footnote; Seemingly, the intent of Admur is that even initially one may Daven Mincha during Beisn Hashmashos in a time of need, and not that simply one is not to protest those who are lenient in a time of need. VeTzaruch Iyun. See Biurim ibid p. 66
 Siddur Admur in Seder Hachnasas Shabbos; Darkei Moshe 233 that Maharil would Daven Mincha close to Tzeis Hakochavim in a time of need, brought in M”A 233:6; Mor Uketzia 233; Shoel Umeishiv Giumel 247; Kitzur SHU”A 69:2; Ketzos Hashulchan 26:1; Or Letziyon 1:20; Shevet Halevi 9:48; M”B ibid also permits in time of need however he limits this to a case of “great need” and only until 15 minutes before Tzeis [according to Rabbeinu Tam]; Piskeiy Teshuvos ibid
The reason: As we see that the Sages permitted one to perform Rabbinical Melacha during Bein Hashmashos of Friday in a time of need, and for the need of a passing Mitzvah. The same then applies regarding Mincha, which is only a Rabbinical obligation. [Admur ibid; See Admur 261:2]
 M”B 233/14
 Mor Uketzia 233; Shoel Umeishiv Giumel 247; Shearim Hametzuyanim Behalacha 69:1; Or Letziyon 1:20; Shevet Halevi 9:48; Eiynayim Lamishpat Brachos 27a; Piskeiy Tehsuvos 233:6
 Admur does not make clear as to what is defined as a time of need to allow delaying Mincha until after sunset. See Admur 90:11 that Davening within the Zeman is more important than Davening with a Minyan.
 M”B 233:14
 Pashut! See Michaber 233:1; Admur in Seder ibid
 See Taamei Haminhagim in Sefer Zichron Tov; The Rebbe Davened Mincha with a Minyan after nightfall during many of the days between the 19th of Kisleiv 5746 and 8th of Shevat