Redirecting login to another website

I’m making a site for a client. He has already a site with an user system, where the users log in to a “back end” on a different web-page. So say the site’s adress is https://www.companyname.com, and there you can find a login-form wich sends you to https://www.theservicethecompanyoffers.com ?? I want this users to be able to log in from the new website I’m creating, but I’m a little lost, I think.
After some research I think I need to first import the users to the wp database, and then redirect the login url to https://www.theservicethecompanyoffers.com. Is this right? In that case, how do I redirect the users there?
And by the way, I’m using a child theme ??