Bit confusing post there but will try help on this..
Dreamweaver is a programing tool to code websites or applications with. Joomla is a CMS - Content Mangement system. Adobe Business Catalyst is the BC CMS (more then just a cms).
You can choose to develop BC sites on Dreamweaver or other applications like Coda2, Sublime Text 2 etc.
Best thing to do is not just try copy their old site, likely lots of issues, badly made, strange things etc. Rebuild, do it right, web standards, work to help improve the online business. etc
But if you export their customers from joomla into an excel spreadsheet you can download the import spreadsheet from BC for the CRM and get the content into the format BC needs from the joomla one and then import.
Joomla addons, custom PHP code etc of course wont run on BC.
Hope that helps.