You can save images and export containers before changing the storage driver
docker save myImage1 > myImage1.tar
docker export myContainer1 > myContainer1.tar
Then you have to load images and import containers after having changed the storage driver
docker load -i myImage1.tar
docker import /path/to/myContainer1.tar
Be careful that, as for official documentation:
the docker export command does not export the contents of volumes
associated with the container. If a volume is mounted on top of an
existing directory in the container, docker export will export the
contents of the underlying directory, not the contents of the volume.
Refer to Backup, restore, or migrate data volumes in the user guide
for examples on exporting data in a volume.