How do I create a new list using existing contacts, so that unsubscribes from the new list do not affect the original list?

How do I create a new list using existing contacts, so that unsubscribes from the new list do not affect the original list?

Hi,

We have a mailing list of customers (Service_A_List) for our main brand. Those customers have opted in to be mailed about other services we offer.
We want to launch a new service that will be publicised to the our existing customers, and will recruit new customers through other means. The new contact list will be Service_B_List.
I want to copy all the contacts from Service_A_List to Service_B_List.
From this point on, if someone unsubscribes from one list it does not affect the other.

How do I do this?