I'm not 100% sure I understand the circumstances you describe. I think your client faile the UC live gateway conditions and you were paying HB. If that's the case then ignore the Live to Full migration, I think it's a red herring that makes this seem more complex than it has to be.
The easiest way to think of this is: would your client have to make a new claim for HB? If not and a COA form will suffice then there is no trigger and they won't have to claim UC(FS) until there's another trigger of some kind.
If I've misunderstood your scenario, accept my apologies, let me know and I'll try again!
