This walkthrough goes over moving Unifi access point to another Unifi controller. To remove APs from a Unifi Controller you need to reset the APs and then either discover them or manually SSH set-inform the devices.
On the new controller try to discover the now factory reset APs and with any luck they will show up. However in big environments I typically can never get them to be discovered so I will show you the manual method.
Find the IP of the AP (You can easily grab this by looking at old controller OR using advanced IP Scanner. Note: match MAC address if scanning)
Putty into the AP (Launch Putty type IP, and Username/Password is factory ubnt/ubnt)
Adopt AP in new controller webpage
We are now done moving Unifi access point on to the new Controller, and as a result, will be in the device list. From here you will be able to manage it, upgrade firmware, and do all the configuration options needed.