Cross Domain Query – eCommerce Website

I've a client who is insisting on having a second website for successful purchase of the product. Is it good from user point of view?

To elaborate, a user will view the product on abc but when he tries to purchase it he'll be redirected some other cross-domain website such as xyz.abc for successful payment (this will be payment gateway kind of website) but he'll stay and exit from the cross domain but not from the original website.

Is this right? Should he do it? He asked me, but I was little confused. I mean big brand like Amazon don't do this kind of stuff. If not, what should I recommend him?

Thanks.