Code Crafters

I would like to move one of the domains and its e-mail accounts to another server already running AMS. What's the best way to move accounts without copying/pasting the entire Code-Crafters folder?

1) You can copy the "config\accounts" folder to a new Ability Mail Server installation on another computer. You may also choose to copy the whole "config" directory to replicate all the server settings.
2) Edit the accounts INI files (domains.ini, users.ini and mailinglists.ini etc.) as appropriate to remove the unused domains, users etc. on each of the mail servers.
3) Delete the unused "config\accounts\<domain>" folders for unused domains on each mail server.

So, based on what you said, I could also...

1) Cut and paste a folder (domainname.com, for example) under the the config\accounts folder from one server to the other.
2) Cut and paste the related info from domains.ini and users.ini from one server to the other.

I should have both servers shut down when I do this, right?

Yes, that's right you can simply move the appropriate settings that you need. Ideally both mail servers would be offline but its perfectly fine to do this while they are online as long as you don't edit any settings while they are online that might overwrite the ones you're editing; the edited changes will be noticed every 30 mins by default (general settings). Note also that any WebMail users can also change settings while you are editing the INI files so it probably is best to at least disable WebMail while you make the changes.