To move LAM (Pro) from one server to another please follow these steps:
Install LAM (Pro) on your new server
Copy the following files from the old server to the new one (base directory for RPM/DEB is /usr/share/ldap-account-manager/):
config/selfService/*.* (needed for LAM Pro only)
The files must be writable for the webserver user.
Open LAM (Pro) login page on new server and verify installation.
Uninstall LAM (Pro) on old server.