Sorry if the title doesn't make sense of my question, it doesn't seem to be working too well while searching either

Our company has acquired one of our wholesale customers site/domain in exchange for a debt. They sell exactly the same things we do, their domain shows up higher on SE results than ours, and they have been on the web longer as well. The biggest problem is our packaging/labels all say our existing domain, and I am personally quite fond of the shopping cart we have been using on our site as opposed to the new site's (yahoo)

My question is... Is there a way to forward the new domain, along with it's search engine results/rankings/etc to our existing site/domain?

I did find info about 301 redirect, but none of the info applied to my case so any help would be highly appreciated!