Mapping user to filesystem user when UID's mismatch?

Say I have a user named *user* with UID *1001* on one system and the same user (named *user*) with another UID, let's say *1002*. If I unplug the disk drive from the second system and plug it into the first, is there an elegant way to act as if UID 1002 on the newly added drive is the same as UID 1001 on the current system (without actually scanning the file tree and chown'ing 1002 to 1001)?