cognito verification link to validate users

Hi team,

I have a Cognito user pool with 3 Groups, I want to create users inside Groups as System Administrators:

1. the system Admin will fill out a form about client's: given name, surname, email address + some custom attributes
2. when sending the form (invitation), my lambda function should create the user inside my Cognito user pool Group with all the above attributes.
3. the client will receive a link via email to validate the invitation
4. when the client clicks the link (custom Domain link), he validates the invitation

I created a lambda function that creates the user in the Cognito user pool and then added it inside the group (using adminCreateUser and adminAddUserToGroup AP calls)

const params = {
    UserPoolId: USER_POOL_ID,
    Username: event.email,
    UserAttributes: [
      {
        Name: "email",
        Value: event.email,
      },
      {
        Name: "given_name",
        Value: event.givenName,
      },
      {
        Name: "family_name",
        Value: event.familyName,
      },
    ],
  };

  try {
    const result = await cognitoIdentityServiceProvider
      .adminCreateUser(params)
      .promise();

I also configured the Cognito to send a link email

On "Message customisations" page> "Do you want to customize your email verification messages?" > "Verification type" => I chose "Link" option

After lambda has run, the user is created with Confirmation status = Force change password

and the email I received looks like this :

Subject = Your temporary password
Body = Your username is myEmail@gmail.com and temporary password is Hc>sP40782HNz%.

so I expected to receive a Link and when the client click the link it validate the invitation (point 4 above) then the client becomes validated inside my user pool.

But I did not receive a link, how can I achieve points 3 and 4?

I just want after creating the user and adding it to a group, to make it valid in Cognito once he clicks the emailed link