Is there an Inyan to rise while saying “Elokeinu” when bentching with a Minyan?
There is a source for this custom. The Previous Rebbe, as well as the Rebbe did so.
שקו״ט בזה – ראה שו״ת חת״ס או״ח נא. א״א מבוטשאטש קצב.
וראה סה״ש תרצ״א ע׳ 142.
P.S. There are videos that show the Rebbe raising his holy body slightly when saying “Elokeinu”.
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