The method described in this post written in January 2013 no longer works. I recently came up with a new way of sharing Brain Workshop history between multiple machines through Dropbox. Refer to this post for details.
Although it's still somewhat buggy, Brain Workshop is a great Dual-N-Back working memory trainer. I've had problems running it in Debian with Pulseaudio installed, so I decided to install it in Arch Linux through the Brain Workshop pkgbuild in AUR.
My ArchLinux system uses plain old ALSA, and the crashes in Brain Workshop now only occur once every 15 or so sets (compared to once every 3 sets previously when using Pulseaudio).
On ArchLinux, brain workshop stores training history in the text file ~/.brainworkshop.stats, but this file won't exist immediately after a fresh install.
From your machine containing your existing brain workshop training history, create a symlink pointing to a folder in Dropbox.
ln -s ~/.brainworkshop.stats ~/Dropbox/brainworkshop/
This will create a linked copy of your history file in the folder "brainworkshop" in Dropbox.
On your machine with the new Brain Workshop install, create a symlink from Dropbox to your user directory:
ln -s ~/Dropbox/brainworkshop/.brainworkshop.stats ~/
Now, if you start your fresh install of Brain workshop and press 'G' to see a graph of your training history, it will show your progress instead of 'Insufficient Data, 2 days needed'.