Frederick Andrews is most likely a pseudonym for the real boy in the story. Later in the lessons Haanel mentions a company and its founder without naming them so this leads me to believe that he protected the identity of people he used.

It also could just be a made up story used to illustrate affirmations.

Sick of typing my answer & it not being posted! Here I go again! The boy is not fictional! Frederick later became a minister of Unity Church. The church founded by Charles & Myrtle Fillmore, who both healed themselves in the same way in a couple of years & so people tended to gather with them after church to discuss such things & it developed into Unity Church! Headquarters I think is still in Missouri where Frederick attended! If you want to call them, I'm sure they would love to help you! I am an attendee of a Unity Church.