On a regular shabbas the teffilah of retzei vhachlitzainu in shmoneh esri has three variations:
In maariv it is בה .
In shachris and musaf it is בו.
In mincha it is בם.
There is a reason for this difference (gematria or a parable of a bride).
My question is, when Yom Kippur falls on shabbas, my machzor uses בו in neilah. Is there a reason for this (other than the editors forgot to differentiate)? Shouldn't it say בם since it is after mincha?
In the Nusach Ari (Chabad) Siddur it says בו as in מוסף, the simple understanding is that נעילה has all similarities to מוסף than of מנחה; Namely, we (Chabad) say מי כמוך אב הרחמים (instead of הרחמן) by מוסף not by מנחה (unless it's Shabbos) but we also say it by נעילה. We (all נוסחאות that I've seen) say the Kedusha that is said by מוסף (rather than the one said by מנחה).
I would indicate that the Lubavitcher Rebbe writes on the page margin that לכאורה it should be בם (just like Mincha וצריך עיון. Some Chabad Machzorim incorporated בם in the actual text, but it was never changed during the Rebbe's time. (So some say בו and some say בם.)
