flutter web save page stack after refresh a page

Question

I am trying to restore pages stack after a browser refresh button pressing. Using onGenerateRoute on MaterialApp I can restore the single page, even with arguments using SharedPrefences api and Firestore data but when I press the browser back button it goes to the home page. How can I save the flutter page stack or at least only the branch of the current page in the stack? This is an example of onGenerateRoute implementation:

if (settings.name == ProductEditScreen.routeName) {
  final args = settings.arguments != null
      ? settings.arguments as ProductEditScreenArguments
      : null;
  return MaterialPageRoute(
    settings: RouteSettings(name: ProductEditScreen.routeName),
    builder: (context) {
      return settings.arguments != null
          ? ProductEditScreen(
              arguments: ProductEditScreenArguments(
                args!.product,
                args.store,
                args.locations,
              ),
              setCurrentPageData: () async {
                SharedPreferences prefs =
                    await SharedPreferences.getInstance();
                //prefs.setString("sessionToken", user!.sessionToken!);
                prefs.setString("productId", args.product.id!);
                prefs.setString("storeId", args.store.id!);
              },
            )
          : FutureBuilder<CurrentPageData>(future: () async {
              SharedPreferences prefs =
                  await SharedPreferences.getInstance();
              prefs.getString("sessionToken");
              String? storeId = prefs.getString("storeId");
              String? productId = prefs.getString("productId");
              List<Location> locations = await EntityControllers
                  .locationController
                  .readAll()
                  .then((locations) => locations.cast<Location>());
              Store store = (await EntityControllers.storeController
                  .readOneByAttribute("id", storeId!)) as Store;
              Product product =
                  await ProductController.productQueryController(
                      productId!);
              return CurrentPageData(
                // sessionToken: user!.sessionToken!,
                screenName: ProductEditScreen.routeName,
                data: {
                  "store": store.toJson(),
                },
                dataEntity: {"product": product},
                dataList: locations.map((e) => e.toJson()).toList(),
              );
            }(), builder: (BuildContext context,
              AsyncSnapshot<CurrentPageData> snapshot) {
              if (snapshot.connectionState == ConnectionState.waiting) {
                return Center(child: CircularProgressIndicator());
              }
              if (snapshot.hasData) {
                Store store =
                    Store.fromJson(snapshot.data!.data!["store"]!);
                List<Location> locations = snapshot.data!.dataList!
                    .map((location) => Location.fromJson(location))
                    .toList();
                Product product =
                    snapshot.data!.dataEntity!["product"] as Product;
                return ProductEditScreen(
                  arguments: ProductEditScreenArguments(
                    product,
                    store,
                    locations,
                  ),
                  setCurrentPageData: () async {
                    SharedPreferences prefs =
                        await SharedPreferences.getInstance();
                    //prefs.setString("sessionToken", user!.sessionToken!);
                    print("screen session token:");
                    prefs.setString("storeId", store.id!);
                    prefs.setString("productId", product.id!);
                  },
                );
              } else {
                if (snapshot.hasError) {
                  print(snapshot.error);
                }
                return DashboardScreen();
              }
            });
    },
  );
}

Before ProductEditScreen page there is ProductListScreen page. I need to put them into the stack.