My employer used to go by another name years ago, and use a different domain. Since then, they moved to a different domain, and then another domain. All 3 domain names are set up so that the DNS resolves to the same website. The oldest domain still has old backlinks, so it has some value. Doing a Google search for certain terms shows that this old domain is still showing up as a separate website in Google's index. Yet the intermediate domain has been "folded" into the current domain.
How do we instruct Google to consider any links to the oldest domain as links to the newest domain? Do we have to set up a separate webserver with a permanent redirect?