When a player gets into the Hall of Fame. Who decides what team the player goes in as? Is it the player or the NFL?

Like in the case of Brett Favre he played for the Falcons, Packers and now the Jets. When he gets elected which of course he will. Does he have to go in as a Packer or could he go in as Jet if he chooses?

That would be a great sentiment to give Greenbay if he decided he wants to go in as a Jet!!