I have used rclone (
rclone.org) to copy files from cloud services to local storage, then to copy files up to a shared drive on GWS. I also use rclone to pull backups of various GWS shared drives to local storage. Rclone supports both Box and Google.
The recipe is pretty simple:
1. download and install rclone on a local machine with sufficient storage for your migration
2. Create Box and Google rclone configurations. Rclone has good documentation to help on this.
3. Use rclone to mount your Box drive
4. Copy the files to a local directory.
5. You can unmount the Box drive after the copy is completed. Considering the magnitude of your move you may want to do this in small bites.
6. Use rclone to mount the GWS shared drive
7. Copy the files now in your local storage up to the shared drive. Again this will take time, maybe a lot of time
8. Repeat as necessary to copy all the files.