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?