[Mailman-Users] migrating lists from one host cPanel to another

I manage several non-profits that use Mailman lists. One of them may be moving their domain from HostGator to BlueHost, both having cPanels. Can you direct me how I can migrate the lists from one to the other without having to build them from scratch? The domain will end up being the same, although I have a temporary name for the new one. Thank you in advance.