diff --git a/Cargo.lock b/Cargo.lock
index ade3a5a..1815ac7 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -1508,6 +1508,8 @@ dependencies = [
  "image",
  "log",
  "muda",
+ "objc2 0.6.5",
+ "objc2-app-kit 0.3.2",
  "pollster 1.0.1",
  "rfd",
  "serde_json",
diff --git a/apps/gridcraft/Cargo.toml b/apps/gridcraft/Cargo.toml
index c867d24..cd8311b 100644
--- a/apps/gridcraft/Cargo.toml
+++ b/apps/gridcraft/Cargo.toml
@@ -42,3 +42,13 @@ muda = { version = "0.21", default-features = false }
 # by PdfCraft and PhotoCraft) registers the handler (Objective-C interop needs unsafe, which our
 # workspace forbids) behind a safe API. Pinned exactly: review the diff before bumping.
 fmv-macos-events = "=0.1.0"
+
+# tests/mac_menu_appkit.rs: reads AppKit's menu bar back. Already in Cargo.lock (muda, winit);
+# pinned exactly to the same versions.
+[target.'cfg(target_os = "macos")'.dev-dependencies]
+objc2 = "=0.6.5"
+objc2-app-kit = { version = "=0.3.2", default-features = false, features = ["std", "NSApplication", "NSMenu", "NSMenuItem", "NSResponder"] }
+
+[[test]]
+name = "mac_menu_appkit"
+harness = false
diff --git a/apps/gridcraft/src/native_menu.rs b/apps/gridcraft/src/native_menu.rs
index b127543..1469242 100644
--- a/apps/gridcraft/src/native_menu.rs
+++ b/apps/gridcraft/src/native_menu.rs
@@ -215,6 +215,7 @@ impl NativeMenu {
         ]);
         let _ = menu.append(&app_menu);
         let mut theme_items = Vec::new();
+        let mut window_menu = None;
         for (title, entries) in tree() {
             let sub = Submenu::new(title, true);
             for (label, id, acc) in entries {
@@ -237,8 +238,17 @@ impl NativeMenu {
                 let _ = sub.append(&item);
             }
             let _ = menu.append(&sub);
+            if title == "Window" {
+                window_menu = Some(sub);
+            }
         }
         menu.init_for_nsapp();
+        // NSApp's windowsMenu is where macOS adds Move & Resize, Fill and Center, the targets of the
+        // system tiling shortcuts (Fn+Ctrl+arrows, Fn+F). Only once the menu is NSApp's: muda looks
+        // the submenu up in the installed main menu.
+        if let Some(window) = window_menu {
+            window.set_as_windows_menu_for_nsapp();
+        }
         let (tx, rx) = channel();
         let ctx = ctx.clone();
         MenuEvent::set_event_handler(Some(move |e: MenuEvent| {
diff --git a/apps/gridcraft/tests/mac_menu_appkit.rs b/apps/gridcraft/tests/mac_menu_appkit.rs
new file mode 100644
index 0000000..e713f66
--- /dev/null
+++ b/apps/gridcraft/tests/mac_menu_appkit.rs
@@ -0,0 +1,34 @@
+//! The macOS menu bar as AppKit sees it, on the main thread (`harness = false`): install it through
+//! the real muda backend (`src/native_menu.rs`) and read NSApp back. The Window menu must be NSApp's
+//! `windowsMenu`: that is where macOS adds Move & Resize, Fill and Center, the targets of the system
+//! window tiling shortcuts (Fn+Ctrl+arrows, Fn+F), and lists the open windows (#716).
+
+// The app's own module, built into this test (cargo builds harness = false tests with cfg(test), so its
+// unit tests compile here too without a harness to run them).
+#[cfg(target_os = "macos")]
+#[path = "../src/native_menu.rs"]
+#[allow(unused_imports, dead_code)]
+mod native_menu;
+
+#[cfg(target_os = "macos")]
+fn main() {
+    use objc2::MainThreadMarker;
+    use objc2_app_kit::NSApplication;
+
+    let mtm = MainThreadMarker::new().expect("harness = false runs on the main thread");
+    let nsapp = NSApplication::sharedApplication(mtm);
+    nsapp.finishLaunching();
+
+    let ctx = egui::Context::default();
+    let _menu = native_menu::NativeMenu::install(&ctx);
+
+    let bar = nsapp.mainMenu().expect("a main menu");
+    let tops: Vec<String> = (0..bar.numberOfItems()).filter_map(|i| bar.itemAtIndex(i)?.submenu()).map(|m| m.title().to_string()).collect();
+    assert_eq!(tops, ["GridCraft", "File", "Edit", "View", "Insert", "Format", "Tools", "Data", "Window", "Help"]);
+    assert_eq!(nsapp.windowsMenu().map(|m| m.title().to_string()).as_deref(), Some("Window"), "AppKit knows the Window menu");
+
+    println!("mac_menu_appkit: ok");
+}
+
+#[cfg(not(target_os = "macos"))]
+fn main() {}