One of the bi-pin lamp socket is damaged and I need to replace it. I
bought new sockets but here the problem.

The damaged socket has three wires (two white and a silver)
Two wires, silver/white, are connected at the front of socket, same as
new one, but other white one goes inside of the socket in the back of
socket. In the newer one there's no place for it.

Do I need to open it up and insert that wire there somehow? I'm
confused. The fluorescent lamp fixture is really old.

Please help.