with regard to a reward booking made with ba using avios, this is not a cancellation tho. it is a change and a BA agent should be able to do it without cancelling the original booking and creating a new one. you change from J to F, and will pay any additional cash & avios required. you would keep the same booking reference. there will be a change fee which is $55 per person.

you could do it the manual way of cancelling the J reward (there will be a $55 per person cancellation fee) and booking the F reward online. there are risks doing that if doing the cancellation first, sometimes the reward booking refund is not instantaneous for example. if you wanted to make the new f booking first you would need the avios to cover both. tbh doing it as a change as noted above is the easier option.