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May one count by Bein Hashmashos?
It is disputed amongst Poskim as to whether one may initially begin counting from after sunset or if he must wait until after nightfall. Practically, it is proper for every person to avoid counting the Omer during Bein Hashmashos, until after nightfall. Nevertheless, in the event that one accidently counted the Sefira by Bein Hashmashos he has fulfilled his obligation and is not required at all from the letter of the law to repeat the count after nightfall, even without a blessing. (Nevertheless, it is proper to recount after nightfall without a blessing even in such a case.) [If one did not do so, see Halacha 22 that he may nevertheless continue counting with a blessing the following nights.]
 Admur 489/12-13; See Igros Kodesh 19/272 [printed in Shulchan Menachem 3/1]
 Some Poskim rule [Tosafus Menachos 66a; Smag 200 in name of Rashba; Rosh 10/40; Tur; See Michaber 489/3] that it is permitted to count the Omer with a blessing during Bein Hashmashos even though Bein Hashmashos is considered in question as to whether it is the beginning of the coming night or the end of the past day. Now, although it seems problematic to say “Today is the 2nd day” when in truth it may still be the 1st day, nevertheless, since today the counting of the Omer is only a Rabbinical command, therefore one may be lenient, as is always the rule regarding a doubt by a Rabbinical command. [Safek Derabanan Lihakel] Other Poskim [Tosafus ibid; Ran Pesachim 28; Taz 489/5] however argue on this and rule that Lechatchilah one may not enter himself into a doubt even by a Rabbinical command, and thus one is to delay the counting until after nightfall when it is definitely night. [Admur 489/12]
 So is done by the meticulous and so is proper to be followed by every Jew. [Admur ibid; Michaber 489/2] However the widespread custom [in those times] is like the first opinion to count the Omer during Bein Hashmashos, after sunset. [Admur ibid; Bach 489; Chok Yaakov 489/12]
What is one to do if he is Davening with a Minyan that is counting Sefira before Bein Hashmashos: See Halacha D!
Erev Shabbos: Some communities are accustomed on Erev Shabbos to Daven Maariv early and recite Sefiras Haomer before nightfall. [Maharshal 13; Leket Yosher in name of Terumos Hadeshen; Mateh Moshe 673 in name of Raavan; Aruch Hashulchan 489/7; Shraga Hameir 6/41; See Piskeiy Teshuvos 489/12 footnote 61]
 Admur 489/13; M”A 489/6
The reason: As he has already fulfilled his obligation, as although Bein Hashmashos is held in question if it is considered night, nevertheless by a Rabbinical command we are lenient in case of doubt. [Admur ibid; Elya Raba 489/10]
 Lit. Tov
 Admur ibid; [parentheses in original]; Elya Raba ibid; P”M 489 M”Z 5; Kaf Hachaim 489/41
The reason: It is proper to recount after nightfall without a blessing in order to suspect for those opinions who say that even today the counting of the Omer is a Biblical obligation [and in their opinion one does not fulfill his obligation in case of doubt]. [Admur ibid]