Yes, you can make this FE, Using RemoteEvents

example:

-- Server
local remote = game.ReplicatedStorage.RemoteEvent

remote.OnServerEvent:Connect(function(player, arg) -- Got player fired the event, and argument send
	print("I fired by: " .. player.Name .. " this player send me the argument: " .. tostring(arg))
	if arg == "CreatePart" then
		print("Creating a part...")
		local part = Instance.new("Part")
		part.Name = "Part - Remote"
		part.Parent = workspace
		print("Created Part")
	end
end)

-- Client
local remote = game.ReplicatedStorage.RemoteEvent

script.Parent.MouseButton1Click:Connect(function()
	remote:FireServer("Hi") -- Here you dont need to send player.
end)

For your problem is here fixed script:

Create a RemoteEvent in ReplicatedStorage, now insert a ServerScript in ServerScriptService.

Client(Local Script, Fire Event)

local event = game.ReplicatedStorage.RemoteEvent -- Remote Event Location

function click()
    local mess = script.Parent.Parent.TextBox -- Removed the .Text
    script.Parent.Parent.TextBox.Text = "Please Wait 5 Seconds"
    event:FireServer("ChangeText",mess.Text) -- Text and argument send here to server.
    script.Parent.Parent.TextBox.Text = ""
end
script.Parent.MouseButton1Click:Connect(click)

Server Script(Script, Remote Event Script)

local event = game.ReplicatedStorage.RemoteEvent -- Remote Event Location

event.OnServerEvent:Connect(function(player,arg,text) -- On fire event
	if arg == "ChangeText" then -- Check for argument
		-- Change Text
		workspace.Message.SurfaceGui.Frame.words.Text = tostring(text)
		wait(5)
		workspace.Message.SurfaceGui.Frame.words.Text = ""
	end
end)

Hope it helped :)

Wiki pages:

Remote Events / Functions

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