@ChristopherSuess, there are some good comments and questions, but I am not sure if they answered your actual question. If I missed it, and they did, my apologies to the respondent.
The Arrow of Light Award is a rank badge, not a type of Den. You will note that the Scout Shop does not sell an AOL Handbook. What you are calling an AOL Den, is actually a 5th grade, or 2nd year, Webelos Den with the same advancement and award opens as the den for 4th grade Webelos. No matter which of the 2 Dens you place the Scout in, the Den Leader can enter all of his Adventure information for the Webelos Badge core adventures, Arrow of Light Award core adventures, and Webelos Elective adventures. So moving the Scout has no affect on what is available to him or her.
From what you have said, the Scout in question has not completed 4th grade, so he/she is at leas 10 years old and has been active in a Webelos Den for at least 3 months so they can start on their 6 months time for Arrow of Light Requirement #1. I am sad he/she is not having fun with the former Denmates and wanting to eave early, but that is the family’s choice. I wish them well.