A technique for managing access to files by different data storage systems includes a data storage system generating an E-FSID (export FSID) for a file system in addition to a conventional FSID and providing the E-FSID in file handles that the data storage system generates for providing clients with access to the file system. The E-FSID is shared between/among different data storage systems, with each data storage system including data for cross-referencing the E-FSID to a respective local FSID for the file system. Because the E-FSID for a file is the same across different data storage systems, file handles continue to work after failover, migration, and other transitions.