There's an easy way to get the docker daemon to handle this for you.
stop docker
$ service docker stop
add this line to /etc/default/docker
# Use DOCKER_OPTS to modify the daemon startup options.
DOCKER_OPTS="-g /<new destination>/docker/"
start docker
$ service docker start
verify the docker files and folders are created in the new destination
remove /var/lib/docker
/var/lib$ sudo rm -rf docker
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