How do I make clothing change globally instead of locally?

Hey, so I'm making a GUI that allows you to change shirt upon pressing a button. After finishing up I went to test on a local server so I could see the script working on other players, but I could see the script only worked locally (on the player who pressed the button's screen) and his clothes were being removed. How would I fix this?

script.Parent.Activated:Connect(function()
    local player = script.Parent.Parent.Parent.Parent.Parent --plr name
    local p = script.Parent.Pants.PantsTemplate --pants are being stored in parent
    local s = script.Parent.Shirt.ShirtTemplate --shirts are being stored in parent
    local foundShirt = player.Character:FindFirstChild("Shirt") -- Tries to find Shirt
    if not foundShirt then -- if there is no shirt
        print("No shirt found, creating for "..player.Name)
        local newShirt = Instance.new("Shirt",player.Character)
        newShirt.Name = "Shirt"
    else if foundShirt then -- if there is a shirt
        print("Shirt found, reconstructing for "..player.Name)
        player.Character.Shirt:remove()
        local newShirt = Instance.new("Shirt",player.Character)
        newShirt.Name = "Shirt"
    end
    end

I have this hooked up to a text button. Thanks.