A technique converts a stream of virtual volume block numbers (vvbns) into a hybrid virtual volume (vvol) file system containing both physical volume block numbers (pvbns) and vvbns. The stream of vvbns is illustratively embodied as a file system data stream of a vvol that is transferred by a source to a destination in accordance with image transfer operations, such as volume copying and synchronous or asynchronous mirroring. Transfer of the vvol involves converting a file system on the source vvol into the file system data stream (i.e., a "pure" vvol stream), where all blocks of the vvol are represented by vvbns. The file system data stream is then transferred to the destination, where the vvbns of the pure vvol stream blocks are converted to pvbns of a hybrid stream.