Did the Mittler Rebbe author a Shulchan Aruch?[1]

Yes. It is recorded in the name of Rabbi Menachem Mendal, the son of the Rebbe Maharash, that the Mittler Rebbe compiled a Shulchan Aruch on all four books of the Tur. Likewise, he also wrote a very elaborate commentary on the Shulchan Aruch of the Alter Rebbe, similar to his book Toras Chaim which was written on the Alter Rebbe’s Torah Or. The Chassidim were accustomed to grab these manuscripts [for their own learning], some grabbing one page, another a half of a page, and it caused it to not remain printable.

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[1] Maaseh Avosaiy, from Sefer Migdal Oz letter 80 p. 189; Otzer Sippurei Chabad 18 p. 43 [The above Sefer was compiled by Rav Shia Mondshine, and as per the testimony of Rav Berel Levin, the librarian of the Rebbe’s library, it is a most trustworthy source. This particular story was written by Rav Azriel Zelig Slonim, probably received from Rav Yechiel Halprin, who was a Chassid of the Rebbe Maharash and Rebbe Rashab]