Marydoll. you're right, the CA period should qualify you for CE scheme if you are going straight from one to the other.
Do you have to wait for payment to come through before being accepted on the scheme? Perhaps proof of having lodged the claim is enough?
I would contact your FAS officer again and ask them this, also ask them to contact SW if they want to verify your qualification (they can verify that you have made a claim by checking their computer records, they have access to SW records) as there are huge delays in processing JB/JA claims due to the unprecedneted increase in Live Register these last few months.