Redirect Connections to a SQL Instance
You can setup a linked server on SERVER_A to SERVER_B and access the databases using four part naming (SERVER_B.database.schema.table). See How to Create a Linked Server in the documentation.

You can also just add a secondary IP address to SERVER_B.

If Server_B is on the same VLAN as Server_A, you can add an alias to its IP address at the client level. But what you want to do is not very feasible.