Here's my datapoint on this
I had made a reservation in July using FHR and then the rates changed so i cancelled the reservation and made a new one. What i saw was was $200 charge and then another $200 credit for the new reservation. So it seemed like the credit did get applied to the new reservation. However in my case, I cancelled the reservation and made a new reservation for the same dates on the same day so that may have factored in. Having said that, the process of cancelling one reservation and creating a new one were completely independent so it makes me think that the credit does get "withdrawn" and "applied" automatically.