At the target side, a first instruction to replicate a first target snapshot-file of a target snapshot-file tree of the target file system is received, the first target snapshot-file of the target file system being associated with a first source snapshot-file of the source file system which has been modified in the source file system. One or more data blocks which are owned by a second target snapshot-file and which are shared between the first target snapshot-file and the second target snapshot-file are identified, the second target snapshot-file being an ancestor of the first target snapshot-file in the target snapshot-file tree. Then, at the target side, ownership of the one or more identified data blocks is transferred from the second target snapshot-file to the first target snapshot-file.