Add Event or dinamically marker in flutter app

Hi folks I'm new with flutter and I building a flutter app with maps and marker, so, I have a class that handles a crud service and receive a specific position, when this class send this position to another class "my maps class" and this class must print a marker in a map. My solution is this, but is very useless because show the previously marker it is not in live. someone can help me pls? thanks.

Class A:

void SaveLatLong() {
    _write(); // write a response query in a file request.txt'
    Home homeMaps = new Home();
    Navigator.of(context)
        .push(MaterialPageRoute(builder: (context) => homeMaps)); // go to another class B
  }

Class B:

class MapsPage extends StatefulWidget {
  static double lat = 0;
  static double long = 0;
  static double Poilat = 0;
  static double Poilong = 0;
  static String PoiName = "";
  @override
  _MapsPageState createState() => _MapsPageState();
}

void getLocation() async {
  final service = LocationService();
  final locationData = await service.getLocation();

  if (locationData != null) {
    MapsPage.lat = locationData.latitude!;
    MapsPage.long = locationData.longitude!;
  }
}

Future<void> _read() async {
  String text = "";
  final Directory directory = await getApplicationDocumentsDirectory();
  final File file = File('${directory.path}/request.txt');
  text = await file.readAsString();
  MapsPage.Poilat = double.parse(text.split(",").first.replaceAll("[", ""));
  MapsPage.Poilong = double.parse(text.split(",")[1]);
  MapsPage.PoiName = text.split(",")[5];
}

class _MapsPageState extends State<MapsPage> {
  _MapsPageState() {
    getLocation();
    _read(); // read to file 
  }
  List<Marker> ListOfMarkers = [
    new Marker(
        width: 45.0,
        height: 45.0,
        point: new LatLng(MapsPage.Poilat, MapsPage.Poilong),
        builder: (context) => new Container(
              child: IconButton(
                  icon: Icon(
                    Icons.add_location_alt_rounded,
                    color: Colors.deepPurple,
                    size: 32,
                  ),
                  onPressed: () {
                    showDialog(
                        context: context,
                        builder: (context) => AlertDialog(
                              title: Text(MapsPage.PoiName),
                            ));
                  }),
            )),
    new Marker(
        width: 45.0,
        height: 45.0,
        point: new LatLng(MapsPage.lat, MapsPage.long),
        builder: (context) => new Container(
              child: IconButton(
                  icon: Icon(
                    Icons.person_pin,
                    color: Colors.blueAccent,
                    size: 42,
                  ),
                  onPressed: () {
                    print('Marker tapped!');
                  }),
            ))
  ];

  @override
  Widget build(BuildContext context) => Scaffold(
        body: Stack(
          children: <Widget>[
            new FlutterMap(
                options: new MapOptions(
                    minZoom: 10.0, center: new LatLng(34.49, 9.34)),
                layers: [
                  new TileLayerOptions(
                      urlTemplate:
                          'https://{s}.tile.openstreetmap.org/{z}/{x}/{y}.png',
                      subdomains: ['a', 'b', 'c']),
                  new MarkerLayerOptions(markers: ListOfMarkers)
                ])
          ],
        ),
      );

  DropdownMenuItem<String> buildMenuItem(String item) => DropdownMenuItem(
        value: item,
        child: Text(
          item,
          style: TextStyle(fontWeight: FontWeight.bold, fontSize: 14),
        ),
      );
}