How can I edit my localscript so it works in a regular script?

So I created a (local)script that places a billboard GUI above your head with some text on it. The problem is, you can only see your billboard GUI and no one else's due to it being placed in a localscript.

I'm pretty sure everything in the script is regular script compatible, but this one line of code is blocking me from placing it in a regular script and I do not know of an alternative for it:

player = game.Players.LocalPlayer

If you'd like to see the script in its entirety:

player = game.Players.LocalPlayer
character = player.Character

script.Parent.FocusLost:connect(function()
		local bg = Instance.new("BillboardGui")
			bg.Parent = character.Head
			bg.Size = UDim2.new(1, 0, 1, 0)
			bg.StudsOffset = Vector3.new(0, 2, 0)
		local frame = Instance.new("Frame")
			frame.Parent = bg
			frame.Size = UDim2.new(1, 0, 1, 0)
			frame.BackgroundTransparency = 1
		local text = Instance.new("TextLabel")
			text.Parent = frame
			text.Position = UDim2.new(0.25, 0, 0.25, 0)
			text.Size = UDim2.new(0.5, 0, 0.5, 0)
			text.Text = script.Parent.Text
			text.BackgroundTransparency = 1
			text.TextColor3 = Color3.new(1, 1, 1)
			text.Font = "ArialBold"
			text.FontSize = "Size24"			
end)

tl;dr: What is a regular script compatible alternative version to LocalPlayer?