A point-in-time copy relationship associates tracks in a source storage with tracks in a target storage. The target storage stores the tracks in the source storage as of a point-in-time. A write request is received including an updated source track for a point-in-time source track in the source storage in the point-in-time copy relationship. The point-in-time source track was in the source storage at the point-in-time the copy relationship was established. The updated source track is stored in a first cache device. A prefetch request is sent to the source storage to prefetch the point-in-time source track in the source storage subject to the write request to a second cache device. A read request is generated to read the source track in the source storage following the sending of the prefetch request. The read source track is copied to a corresponding target track in the target storage.