A Masonic apprentice can improve his memory in the same way that a non-Masonic apprentice can such as staying active mentally. A Masonic apprentice is referred to as an "entered apprentice" by the Masons, which is the first step towards the Masonic degree.
Staying active mentally requires completing activities and exercises that stimulate the brain such as crossword puzzles, learning a musical instrument, or reading a new book genre. Staying social can also help keep memory loss at bay, so Masonic apprentices who meet with other Masons regularly can have better memories. Sleep on a regular schedule also plays an important role in memory functionality.