Use AdminRespondToAuthChallenge with an AWS SDK

    /// <summary>
    /// Respond to an admin authentication challenge.
    /// </summary>
    /// <param name="userName">The name of the user.</param>
    /// <param name="clientId">The client ID.</param>
    /// <param name="mfaCode">The multi-factor authentication code.</param>
    /// <param name="session">The current application session.</param>
    /// <param name="clientId">The user pool ID.</param>
    /// <returns>The result of the authentication response.</returns>
    public async Task<AuthenticationResultType> AdminRespondToAuthChallengeAsync(
        string userName,
        string clientId,
        string mfaCode,
        string session,
        string userPoolId)
    {
        Console.WriteLine("SOFTWARE_TOKEN_MFA challenge is generated");

        var challengeResponses = new Dictionary<string, string>();
        challengeResponses.Add("USERNAME", userName);
        challengeResponses.Add("SOFTWARE_TOKEN_MFA_CODE", mfaCode);

        var respondToAuthChallengeRequest = new AdminRespondToAuthChallengeRequest
        {
            ChallengeName = ChallengeNameType.SOFTWARE_TOKEN_MFA,
            ClientId = clientId,
            ChallengeResponses = challengeResponses,
            Session = session,
            UserPoolId = userPoolId,
        };

        var response = await _cognitoService.AdminRespondToAuthChallengeAsync(respondToAuthChallengeRequest);
        Console.WriteLine($"Response to Authentication {response.AuthenticationResult.TokenType}");
        return response.AuthenticationResult;
    }

        Aws::Client::ClientConfiguration clientConfig;
        // Optional: Set to the AWS Region (overrides config file).
        // clientConfig.region = "us-east-1";

    Aws::CognitoIdentityProvider::CognitoIdentityProviderClient client(clientConfig);

        Aws::CognitoIdentityProvider::Model::AdminRespondToAuthChallengeRequest request;
        request.AddChallengeResponses("USERNAME", userName);
        request.AddChallengeResponses("SOFTWARE_TOKEN_MFA_CODE", mfaCode);
        request.SetChallengeName(
                Aws::CognitoIdentityProvider::Model::ChallengeNameType::SOFTWARE_TOKEN_MFA);
        request.SetClientId(clientID);
        request.SetUserPoolId(userPoolID);
        request.SetSession(session);

        Aws::CognitoIdentityProvider::Model::AdminRespondToAuthChallengeOutcome outcome =
                client.AdminRespondToAuthChallenge(request);

        if (outcome.IsSuccess()) {
            std::cout << "Here is the response to the challenge.\n" <<
                      outcome.GetResult().GetAuthenticationResult().Jsonize().View().WriteReadable()
                      << std::endl;

            accessToken = outcome.GetResult().GetAuthenticationResult().GetAccessToken();
        }
        else {
            std::cerr << "Error with CognitoIdentityProvider::AdminRespondToAuthChallenge. "
                      << outcome.GetError().GetMessage()
                      << std::endl;
            return false;
        }

    // Respond to an authentication challenge.
    public static void adminRespondToAuthChallenge(CognitoIdentityProviderClient identityProviderClient,
            String userName, String clientId, String mfaCode, String session) {
        System.out.println("SOFTWARE_TOKEN_MFA challenge is generated");
        Map<String, String> challengeResponses = new HashMap<>();

        challengeResponses.put("USERNAME", userName);
        challengeResponses.put("SOFTWARE_TOKEN_MFA_CODE", mfaCode);

        AdminRespondToAuthChallengeRequest respondToAuthChallengeRequest = AdminRespondToAuthChallengeRequest.builder()
                .challengeName(ChallengeNameType.SOFTWARE_TOKEN_MFA)
                .clientId(clientId)
                .challengeResponses(challengeResponses)
                .session(session)
                .build();

        AdminRespondToAuthChallengeResponse respondToAuthChallengeResult = identityProviderClient
                .adminRespondToAuthChallenge(respondToAuthChallengeRequest);
        System.out.println("respondToAuthChallengeResult.getAuthenticationResult()"
                + respondToAuthChallengeResult.authenticationResult());
    }

const adminRespondToAuthChallenge = ({
  userPoolId,
  clientId,
  username,
  totp,
  session,
}) => {
  const client = new CognitoIdentityProviderClient({});
  const command = new AdminRespondToAuthChallengeCommand({
    ChallengeName: ChallengeNameType.SOFTWARE_TOKEN_MFA,
    ChallengeResponses: {
      SOFTWARE_TOKEN_MFA_CODE: totp,
      USERNAME: username,
    },
    ClientId: clientId,
    UserPoolId: userPoolId,
    Session: session,
  });

  return client.send(command);
};

// Respond to an authentication challenge.
suspend fun adminRespondToAuthChallenge(
    userName: String,
    clientIdVal: String?,
    mfaCode: String,
    sessionVal: String?,
) {
    println("SOFTWARE_TOKEN_MFA challenge is generated")
    val challengeResponsesOb = mutableMapOf<String, String>()
    challengeResponsesOb["USERNAME"] = userName
    challengeResponsesOb["SOFTWARE_TOKEN_MFA_CODE"] = mfaCode

    val adminRespondToAuthChallengeRequest =
        AdminRespondToAuthChallengeRequest {
            challengeName = ChallengeNameType.SoftwareTokenMfa
            clientId = clientIdVal
            challengeResponses = challengeResponsesOb
            session = sessionVal
        }

    CognitoIdentityProviderClient { region = "us-east-1" }.use { identityProviderClient ->
        val respondToAuthChallengeResult = identityProviderClient.adminRespondToAuthChallenge(adminRespondToAuthChallengeRequest)
        println("respondToAuthChallengeResult.getAuthenticationResult() ${respondToAuthChallengeResult.authenticationResult}")
    }
}

Respond to an MFA challenge by providing a code generated by an associated MFA application.

class CognitoIdentityProviderWrapper:
    """Encapsulates Amazon Cognito actions"""

    def __init__(self, cognito_idp_client, user_pool_id, client_id, client_secret=None):
        """
        :param cognito_idp_client: A Boto3 Amazon Cognito Identity Provider client.
        :param user_pool_id: The ID of an existing Amazon Cognito user pool.
        :param client_id: The ID of a client application registered with the user pool.
        :param client_secret: The client secret, if the client has a secret.
        """
        self.cognito_idp_client = cognito_idp_client
        self.user_pool_id = user_pool_id
        self.client_id = client_id
        self.client_secret = client_secret


    def respond_to_mfa_challenge(self, user_name, session, mfa_code):
        """
        Responds to a challenge for an MFA code. This completes the second step of
        a two-factor sign-in. When sign-in is successful, it returns an access token
        that can be used to get AWS credentials from Amazon Cognito.

        :param user_name: The name of the user who is signing in.
        :param session: Session information returned from a previous call to initiate
                        authentication.
        :param mfa_code: A code generated by the associated MFA application.
        :return: The result of the authentication. When successful, this contains an
                 access token for the user.
        """
        try:
            kwargs = {
                "UserPoolId": self.user_pool_id,
                "ClientId": self.client_id,
                "ChallengeName": "SOFTWARE_TOKEN_MFA",
                "Session": session,
                "ChallengeResponses": {
                    "USERNAME": user_name,
                    "SOFTWARE_TOKEN_MFA_CODE": mfa_code,
                },
            }
            if self.client_secret is not None:
                kwargs["ChallengeResponses"]["SECRET_HASH"] = self._secret_hash(
                    user_name
                )
            response = self.cognito_idp_client.admin_respond_to_auth_challenge(**kwargs)
            auth_result = response["AuthenticationResult"]
        except ClientError as err:
            if err.response["Error"]["Code"] == "ExpiredCodeException":
                logger.warning(
                    "Your MFA code has expired or has been used already. You might have "
                    "to wait a few seconds until your app shows you a new code."
                )
            else:
                logger.error(
                    "Couldn't respond to mfa challenge for %s. Here's why: %s: %s",
                    user_name,
                    err.response["Error"]["Code"],
                    err.response["Error"]["Message"],
                )
                raise
        else:
            return auth_result