Date: September 30, 2015 05:03PM
To the Rescue: The Biography of Thomas S. Monson tells one particular story of his dedication to helping Church members receive all the blessings of the gospel. Church manuals were not allowed into the country, so President Monson memorized the contents of the Church’s General Handbook of Instructions. After arriving in Germany, he asked for a typewriter and began to type up from memory a workable copy. About 30 pages in, he took a break to stretch and walk around the room. He was startled to see, sitting on the self, a German version of the General Handbook of Instructions. How it got there, no one was certain. Needless to say, he was very well versed in the handbook for many years.
Not quite the same as memorizing the BoM. It doesn't sound like he memorized anything. He probably had a written or memorized outline and was just winging it.