How do I transfer the camera?

Zerio, your comment is simple to fix. Change CameraName to current workspace's camera name. Wiki: The center of help and bugs too. Well, guess what there is stuff for what we dont need wiki and we need. In this case, we don't

Let's see your code and point what i've found while reading it:

player = game.Players.LocalPlayer -- Good start, but remember to make it a local variable
-- remember to make script a LocalScript
character = player.Character:Clone()
character.PrimaryPart = character.Torso
character:SetPrimaryPartCFrame(player.Character.Torso.CFrame)
game.Workspace.CurrentCamera.CameraSubject = character.Humanoid -- ... are you serious
game.Workspace.CurrentCamera.CameraType = "Custom"

So, the player would look like this:

local player = game.Players.LocalPlayer

Well, by myself fixing this:

local player = game.Players.LocalPlayer
-- let's replace CHARACTER mess with a model.
modelm = Instance.new("Model", game.Workspace) -- For a player
modelm.Name = player.Name -- This makes the PLAYER's Character model
for _,item in pairs(player.Character:GetChildren()) do -- this will get every character item
item:clone().Parent = modelm -- this works fine
if item.ClassName == "Humanoid" then
 game.Workspace:findFirstChild("CameraName").CameraSubject = modelm.Humanoid
end
end
game.Workspace:findFirstChild("CameraName").CameraType = Enum.CameraType.Custom

Hope this fixes your problem, Thanks, marcoantoniosantos3

As far as I can tell, you problem is that you never set character's Parent to Workspace (or Workspace.CurrentCamera), so the Camera has nothing to attach to.