Character is not a valid member of PlayerGui "Players.USERNAME.PlayerGui"

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#1 
local player = script.Parent.Parent.Parent
local f = script.Parent.ScrollingFrame:GetChildren()
for i=1,#f do
	local face = f[i]
	if face.Name == "Face" or face.Name == "Face1" or face.Name == "Face2" then
		face.MouseButton1Down:connect(function()
			player.Character.Head.face.Texture = face.Image
		end)
	end
end
#2

try

player = game.Players.LocalPlayer

or

player = script:FindFirstAncestorWhichIsA("Player")
#3

Probably It is because when the script runs the Character dont loaded already, just try use

local Character =  Player.Character or Player.CharacterAdded:Wait()

That basically checks if Character exist and If It dont exist It Wait the Character to load

#4 
local players = game:GetService("Players")
local player = players.LocalPlayer or players.PlayerAdded:Wait()
local character = player.Character or player.CharacterAdded:Wait()
local head = character:WaitForChild("Head")

local f = script.Parent:WaitForChild("ScrollingFrame"):GetChildren()

for i, face in pairs(f) do
	if face.Name == "Face" or face.Name == "Face1" or face.Name == "Face2" then
		face.MouseButton1Down:Connect(function()
			if head:FindFirstChild("face") then
				head:WaitForChild("face").Texture = face.Image
			end
		end)
	end
end