Kubernetes - Share content between two containers within same pod

Question

I'm working to extend a JupyterHub installation on Kubernetes (through Helm chart).

I was able to run a pod with 2 containers: singleuser notebook server (namely, A) and a second container (namely, B) used to mount a remote space on the container filesystem.

What I'd like to achieve is to make the content of the B's directory (located at /mnt/space) available in the notebook container A.

Here the current configuration (which is not working)

singleuser:
  memory:
    limit: 2G
    guarantee: 2G
  cpu:
    limit: 2
    guarantee: 2
  extraContainers:
    - name: B
      image: <myimage>
      volumeMounts:
        - name: space
          mountPath: '/mnt/space/'

  storage:
    extraVolumes:
      - name: space
        empty_dir:
          sizeLimit: 20Gi
    extraVolumeMounts:
      - name: space
        mountPath: '/mnt/space:shared'

    capacity: 20Gi
    dynamic:
      pvcNameTemplate: claim-{username}{servername}
      volumeNameTemplate: vol-{username}{servername}
      storageAccessModes: ["ReadWriteMany"]

Volume space seems to be mounted, but it is actually empty. Is there any misconfiguration or something missing?

Thanks in advance.