Yes the non www. is the setup on the server.
The new domain is not yet in search engines, so it's a good idea to make the right move with it.
You can use it to give some sort of an-detail description about the products you have, how students can benefit from it, etc, then link to the old one for purchase, so you can use it for information purposes. The old website has a good rank, but very few pages in Google and that's because the title is very common to other pages, same for the description, while the url is changing.
site:www.micromail.com - Google Search