How to login by getting a string with session cookies?

Question

Sessions

Friends, good day. Suppose, using js on the client side, I received a cookie string for a specific session for an authorized user. How can I take advantage of this, having a session cookie string, and log in as a user remotely? Obviously, I have to make a request to the server and pass the entire line to it in the header, but it doesn’t come out yet (if it is likely that VKontakte will automatically generate a session). I try to do on the example of VKontakte. Tell me how to do it in a more correct direction, or where you can read more about it.
PS I'm doing it without any intentions, I'm just testing my resource.