AFTER EDIT: (With ModuleScript)

let's say this is your module script (remember to put it somewhere the localplayer can access like replicatedstorage or workspace)

local module = {}
module.Model = game.Workspace.Model

function module.CloneModel()
    local modelClone = module.Model:Clone()
    modelClone.Parent = game.Workspace
end
return module

require module from localscript and call it's clone model function

module = require(game.Workspace.ModuleScript)
module.CloneModel()

alternatively, you could get the model from the module script and clone the model in the local script:

module = require(game.Workspace.ModuleScript)
model = module.Model
local modelClone = model:Clone()
modelClone.Parent = game.Workspace

BEFORE EDIT: (With Remote Events)

Create a remote event object in the replicated storage and name it "spawnModel"

fire the remote event to send to the server when the player clicks a button

closeButton = script.Parent.Frame.Button

closeButton.MouseButton1Down:connect(function()
    game.ReplicatedStorage.spawnModel:FireServer("modelNameGoesHere")
end)

Have a function be called when that remote event gets fired spawning the model:

--function that spawns our model
local function spawnModel(player, modelToSpawn)
    local model = game.ReplicatedStorage:FindFirstChild(modelToSpawn)

    --clone the model into the workspace if the model exists 
    if(model)then
        local modelClone = model:Clone()
        modelClone.Parent = game.Workspace
    end
end

--connect the remote event to the function
game.ReplicatedStorage.spawnModel.OnServerEvent:Connect(spawnModel)

User input such as this cannot be detected from the server, it has to be picked up by a local script, you can definitely use a ModuleScript and require it localside, and then pass it onto the server any way you want, but there is no definite way for the server to pick up client input.