How to make user authorization between Login and Game server?

Question

Programming

Hello.
There is a task. The user is authorized in the login server.
Then it needs to be redirected to the game server.
How can I safely redirect it from the login server to the game server so that no one can enter the game using its data with the substitution of links?
So far I see this:
The user has been authorized on the game server,
requests to enter the game server
At this moment, the game server creates a unique session in the database
Then the user transfers this session, and the user transfers it to the game server.
The game server will activate this session.
Is this method safe? The problem is that the login server does not know the user's ip, only the game knows. Therefore, when requesting a game session, the session is only bound to the IP