Alright, let's start by exporting our Firebase Authentication users. We'll use the Firebase Admin SDK and a little script to get a list of all current users.

const admin = require('firebase-admin');
const fs = require('fs');

admin.initializeApp();

const auth = admin.auth();
const filePath = 'users.json';

async function exportUsers() {
  const allUsers = [];
  let nextPageToken;

  do {
    const listUsersResult = await auth.listUsers(1000, nextPageToken);
    listUsersResult.users.forEach((userRecord) => {
      allUsers.push(userRecord.toJSON());
    });
    nextPageToken = listUsersResult.pageToken;
  } while (nextPageToken);

  fs.writeFileSync(filePath, JSON.stringify(allUsers, null, 2));
}

exportUsers().catch(console.error);

This script will save all the user data into a JSON file. We'll use this file in the next steps.

Next, we need to take a look at the exported data and tweak it to fit the new authentication provider's requirements. This might mean changing user records to match fields like email, password hashes, and any extra metadata.

Now, let's get those users into the new system. Most providers, like AWS Cognito or Auth0, have ways to import users in bulk.

For AWS Cognito, for example:

1. Convert the user data to the CSV format that AWS Cognito needs.
2. Use the AWS CLI to import users.

aws cognito-idp admin-create-user-import-job \
  --user-pool-id your_user_pool_id \
  --job-name your_job_name \
  --cloud-watch-logs-role-arn your_iam_role_arn

Time to update your app's authentication code to work with the new provider's SDK or API. Make sure all the methods like sign-in, sign-up, password reset, and verification are working smoothly with the new system.

Test, test, and test again! Make sure the new authentication system is working perfectly. Check if the imported users can log in, reset passwords, and that all their data is still there.

Roll out the changes gradually to avoid any major disruptions. Start with a small group of users if you can. Keep an eye on user feedback and fix any issues that come up quickly.

Let your users know about the migration to the new authentication provider. Give them clear instructions on how to log in, especially if they need to reset their passwords or do anything else.

Dear User, 
We have migrated to a new and improved authentication provider. For your account security, please reset your password using the following link [provided link]. Contact support if you run into any issues.

Best regards,
Your Company