There are many different ways to tackle this problem but before you get started you need to know two crucial things.
1. What brand are the cubicles?
2. Are they wired for electricity?
The brand name will tell people who know what they're doing (not all moving companies do) how to take them apart and reassemble them whether you hire the company that originally installed them or your favorite moving company.
Whether or not they are wired for electricity will tell you whether or not you need to call an electrician to disconnect and reconnect them. Can it be done by someone who isn't an electrician? Sure. But that would also be a good time to check what exactly your insurance policy covers if they accidentally electrocute themselves.
