Narychlo:

import java.awt.*;

import javafx.application.Application;
import javafx.scene.Scene;
import javafx.scene.input.MouseEvent;
import javafx.scene.layout.Pane;
import javafx.stage.Stage;

public class Main extends Application {

    @Override
    public void start(Stage primaryStage) {

        try {
            Pane root = new Pane();
            PointerInfo a = MouseInfo.getPointerInfo();
            Point b = a.getLocation();
            int x = (int) b.getX();
            int y = (int) b.getY();

            root.addEventFilter(MouseEvent.MOUSE_MOVED, e -> {
                try {
                    Robot robot = new Robot();
                    robot.mouseMove(x, y);
                } catch (AWTException e1) {
                    e1.printStackTrace();
                }
            });

            Scene scene = new Scene(root, 800, 400);
            primaryStage.setScene(scene);
            primaryStage.show();

        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    public static void main(String[] args) {
        launch(args);
    }
}

Bude to fungovat jen v okne te applikace a bude nekdy videt, jak se kurzor pohne a vrati zpet...