picker_with_change_notifier.dart

import 'package:flutter/material.dart';
import 'package:provider/provider.dart';


class Parent extends StatelessWidget{
  EmailDomainChangeNotifier emailDomainChangeNotifier =
      EmailDomainChangeNotifier();

  @override
  Widget build(BuildContext context) {
    return Container(
      child: ChangeNotifierProvider<EmailDomainChangeNotifier>(
        builder: (_) => emailDomainChangeNotifier,
        child: HokudaiEmailPicker(),
      ),
    );
  }
}


class EmailDomainChangeNotifier with ChangeNotifier {
  String _emailDomain = '@hokudai.ac.jp';
  String get emailDomain => _emailDomain;

  void changeEmailDomain(String newEmailDomain) {
    _emailDomain = newEmailDomain;
    notifyListeners();
  }
}

class HokudaiEmailPicker extends StatefulWidget {
  @override
  _HokudaiEmailPickerState createState() => _HokudaiEmailPickerState();
}

class _HokudaiEmailPickerState extends State<HokudaiEmailPicker> {
  EmailDomainChangeNotifier emailDomainChangeNotifier;

  @override
  void didChangeDependencies() {
    super.didChangeDependencies();
    emailDomainChangeNotifier = Provider.of<EmailDomainChangeNotifier>(context);
  }

  @override
  Widget build(BuildContext context) {
    var emailDomainList = [
      '@eis.hokudai.ac.jp',
      '@hokudai.ac.jp',
      '@ist.hokudai.ac.jp'
    ];

    return Container(
      child: Row(crossAxisAlignment: CrossAxisAlignment.start, children: [
        PopupMenuButton<String>(
          padding: EdgeInsets.all(0),
          icon: Icon(
            Icons.arrow_drop_down,
            size: 24,
          ),
          onSelected: (String value) {
            setState(() {
              emailDomainChangeNotifier.changeEmailDomain(value);
            });
          },
          initialValue: emailDomainChangeNotifier.emailDomain,
          itemBuilder: (context) => emailDomainList
              .map((v) => PopupMenuItem<String>(value: v, child: Text(v)))
              .toList(),
        ),
        Text(emailDomainChangeNotifier.emailDomain)
      ]),
    );
  }
}

参考

https://qiita.com/kabochapo/items/a90d8438243c27e2f6d9#changenotifierprovider

https://flutter.keicode.com/basics/popupmenubutton.php

スクショ

なぜかStatefulWidgetを使ってしまってる・・