Find where the data is stored that matches your container (as a sudo user, you can access /var/lib/docker/volumes/{container_id}, /var/lib/docker/vfs/dir/{container_id})
Move the data along with your container to the place you want to run.
Use volume mapping when you start the container, so you can have more control of it.
Below are the knowledge could be helpful for you:
A Docker volume permits data to be stored in a container outside of the boot volume (but within the root file system).
A container can be created with one or more volumes by providing a share name passed to the "-v" switch parameter (for example, /dockerdata). This has the effect of creating an entity within the Docker configuration folder (/var/lib/docker) that represents the contents of the volume.
Configuration data on volumes is stored in the /var/lib/docker/volumes folder, with each sub-directory representing a volume name based on a UUID. The data itself is stored in the /var/lib/docker/vfs/dir folder (again based on UUID name).
The data in any volume can be freely browsed and edited by the host operating system, and standard Unix permissions apply.
The use of volumes has advantages and disadvantages. As the data is stored in a standard file system, it can be backed up, copied or moved in and out by the operating system.
The disadvantage here is that the volume name is in UUID format and that makes it tricky to associate with a container name. Docker makes things easier by providing the "docker cp" command that allows files and folders to be copied from a host directory to a container directory path by specifying the container name.
A Docker volume can also be associated with a host directory. This is again specified on the "-v" switch, using a format that separates the host and container paths with a colon, as follows: "-v /host:/container". This method allows persistent data on the host to be accessed by a container.
It would therefore be possible to provide access to external shared storage on an NFS share or LUN by using the volume option to access a host share created on the external storage. This method could also be used to back up the data accessed by containers.