need help transferring old site to new design

I’m new at WordPress. I’ve been able to create a new design for a client at This is one of my urls that I purchased to be able to develop the site off the radar. I’ve used the WPMU theme “Product” for this. My client’s site is How can I transfer the content (ecommerce with a good amount of content, pages and products) to the new design , or transfer the new design to the old site, and publish it under the url?