if your Joomala sites are hosted on the same physical server then you can copu whatever you need using SQL. you can then insert records into your new Joomla system. MySQL allow you to refer to more thna one database in a single statement.

an alternative is to use whatever admn tool your ISP allows you and dump the user tables (+ any other tables that Joomala uses that are required) into a SQL backup and then load that backup into your target db

if you need to do this on a regualr basis consider developing an extension to the system which dumps new, or changed users into another table and clearing down that table periodically. to do that you may need to modify the script that deals with user management, or if the MySQL server you use allows triggers consider doing in there

however this is more a Joomla issue in my books, presumably there must be a site dedicated to supporting that product....