You are obviously a working single parent . ( FIS is a SW payment for family type employees only )
If you decide to move back to your ex , then of course your circumstances change and you need to re-apply for FIS .
However , as your ex has no income , your entitlement to FIS , may continue as normal .
If you are working and you are co-habiting, you should be claiming your single parent tax credit - however , you will lose this tax credit when you move back with your ex .