Tzemach Atlas has a review of Assaf's new (Hebrew) book on hasidim, which contains a chapter detailing the conversion to Christianity of the Ba'al HaTanya's son Moshe:
…Assaf concludes the chapter by unceremoniously taking apart what was said or written about this parsha by Rayatz. Alas Assaf admits that because there is no archival evidence about R. Moshes death in the hospital technically there is a room for the Golus version or even for the version presented by some of the Maskilim that R. Moshe was a clerk in a government office in St. Petersburg. But unfortunately Rayatz not only used extreme creative hyperbola when speaking about this, he also changed the key facts in his own versions of the event.
In 1922 Rayatz wrote a letter to one of the descendants of Zvi Heikin. In the letter there is R. Moshe’s dispute with Christian Theologians (a first mention of this by anybody). R. Moshe is then imprisoned, his cellmate suddenly dies and in the confusion R. Moshe escapes to go in the above mentioned Golus in Volyn area.
In 1942 Rayatz wrote a letter to a Schneerson family member who lived in Montreal. Here R. Moshe is lead by decree to a disputation to occur in Vladimir. The guards that accompany him fall asleep and R. Moshe escapes, and of course the date of the escape is 19 of Kislev! R. Moshe arrives to Orel. In Orel R. Moshe stayed with R. Moshe Leib Yakobson …. R. Moshe then goes to the Golus in Volyn. Assaf points out the Geography and the correlation with the Alter Rebbe himself (besides Yat kislev). The two towns mention[ed] by Rayatz[,] Vladimir and Orel[,] were on Alter Rebbe’s itinerary when he run from Napoleon.…
TA also notes:
… Assaf tells about pivotal moments that he discovered in the archives. R. Moshe attempted (without his family) to join the caravan of his brothers and Alter Rebbe in winter of 1812 when they were fleeing Napoleon’s army. He was arrested by the French in Shklov, the French interrogated him and after concluding that he was a spy, they sentenced him to death. The French then understood that he “was not all there” and let him go.…
…After the war the Schneersons moved to Lubavitch. R. Moshe was with his brothers there even after the incident [conversion] and his family made valiant attempts to protect him from Christians who now claimed his soul. This didn't prevent R. Moshe from writing from Lubavitch that he would rather be a Russian Orthodox than Catholic.…