使用 AWS Cognito 提供的 Lambda 函数来触发自定义消息。首先，需要创建两个 Lambda 函数来处理外部 IdP 帐户注册和传递数据给自定义消息。以下是示例代码：

const AWS = require('aws-sdk');
const cognito = new AWS.CognitoIdentityServiceProvider();

exports.handler = (event, context, callback) => {
  console.log('Received event:', JSON.stringify(event));

  const email = event.request.userAttributes.email;
  const name = event.request.userAttributes.name;
  const provider = event.userName.split('_')[0];

  const params = {
    UserPoolId: event.userPoolId,
    Username: event.userName,
    UserAttributes: [
      {
        Name: 'email',
        Value: email
      },
      {
        Name: 'name',
        Value: name
      },
      {
        Name: 'custom:provider',
        Value: provider
      }
    ]
  };

  cognito.adminUpdateUserAttributes(params, (err) => {
    if (err) {
      console.log('Error:', err);
      callback(err);
      return;
    }

    console.log('Successfully updated user attributes');
    callback(null, event);
  });
};

这个 Lambda 函数是用来更新用户属性的。在此示例中，我们存储了用户的电子邮件地址、名称和他们使用的 IdP 提供程序的名称。

接下来，创建一个 Lambda 函数来触发自定义消息：

const AWS = require('aws-sdk');
const sns = new AWS.SNS();

exports.handler = (event, context, callback) => {
  console.log('Received event:', JSON.stringify(event));

  const userEmail = event.request.userAttributes.email;
  const userName = event.request.userAttributes.name;
  const provider = event.request.userAttributes['custom:provider'];

  const params = {
    Message: `Welcome to our application, ${userName}! You have successfully signed up using ${provider}.`,
    Subject: 'Welcome to Our App!',
    TargetArn: process.env.SNS_TOPIC_ARN
  };

  sns.publish(params, (err, data