Linux – When using NFS, how to make user A on the server appear as user B on the client

I would use rsync as it means that if it is interrupted for any reason, then you can restart it easily with very little cost. And being rsync, it can even restart part way through a large file. As others mention, it can exclude files easily. The simplest way to preserve most things is to use the -a flag – ‘archive.’ So:

rsync -a source dest

Although UID/GID and symlinks are preserved by -a (see -lpgo), your question implies you might want a full copy of the filesystem information; and -a doesn't include hard-links, extended attributes, or ACLs (on Linux) or the above nor resource forks (on OS X.) Thus, for a robust copy of a filesystem, you'll need to include those flags:

rsync -aHAX source dest # Linux
rsync -aHE source dest  # OS X

The default cp will start again, though the -u flag will "copy only when the SOURCE file is newer than the destination file or when the destination file is missing". And the -a (archive) flag will be recursive, not recopy files if you have to restart and preserve permissions. So:

cp -au source dest

According to my limited knowledge, the NFSv4 ID mapping only applies to stat() results and other information sent over NFS itself – that is, to file owners sent by chown, returned by ls or stat, etc.

However, authentication is handled by a lower level – SunRPC – which still uses your numeric UID in the default AUTH_UNIX protocol. So if you're user #12 locally, that's what the server will receive as well.

To avoid this, you'd need an authentication mechanism that supports usernames; Kerberos (AUTH_GSS) might be the only choice here.