Failed to assume role for third-party AWS account using IAM user's access key

I am trying to give a third-party AWS Account access to my AWS Account using Assume Role function with SecurityAudit role, similar to here. I followed the explanation from this to assign the third-party account the role called testing where I will get the trust relationship something like this (which I also added the IAM user of third party since it will access my AWS account using his access key):

{
  "Version": "2012-10-17",
  "Statement": [
    {
      "Effect": "Allow",
      "Principal": {
        "AWS": "arn:aws:iam::thirdparty:root"
      },
      "Action": "sts:AssumeRole",
      "Condition": {}
    }
  ]
}

Then I followed the code from here as follow:

AWSSecurityTokenService stsClient = AWSSecurityTokenServiceClientBuilder.standard()
                                                    .withCredentials(new ProfileCredentialsProvider())
                                                    .withRegion(clientRegion)
                                                    .build();

            // Obtain credentials for the IAM role. Note that you cannot assume the role of an AWS root account;
            // Amazon S3 will deny access. You must use credentials for an IAM user or an IAM role.
            AssumeRoleRequest roleRequest = new AssumeRoleRequest()
                                                    .withRoleArn(roleARN)
                                                    .withRoleSessionName(roleSessionName);
            AssumeRoleResult roleResponse = stsClient.assumeRole(roleRequest);
            Credentials sessionCredentials = roleResponse.getCredentials();

But when the third party run the code it received an error like this:

Exception in thread "main" com.amazonaws.services.securitytoken.model.AWSSecurityTokenServiceException: User: arn:aws:iam::thirdparty:user/TestOne is not authorized to perform: sts:AssumeRole on resource: arn:aws:iam::myaccount:role/testing(Service: AWSSecurityTokenService; Status Code: 403; Error Code: AccessDenied)
    at com.amazonaws.http.AmazonHttpClient$RequestExecutor.handleErrorResponse(AmazonHttpClient.java:1632)
    at com.amazonaws.http.AmazonHttpClient$RequestExecutor.executeOneRequest(AmazonHttpClient.java:1304)
    at com.amazonaws.http.AmazonHttpClient$RequestExecutor.executeHelper(AmazonHttpClient.java:1058)
    at com.amazonaws.http.AmazonHttpClient$RequestExecutor.doExecute(AmazonHttpClient.java:743)
    at com.amazonaws.http.AmazonHttpClient$RequestExecutor.executeWithTimer(AmazonHttpClient.java:717)
    at com.amazonaws.http.AmazonHttpClient$RequestExecutor.execute(AmazonHttpClient.java:699)
    at com.amazonaws.http.AmazonHttpClient$RequestExecutor.access$500(AmazonHttpClient.java:667)
    at com.amazonaws.http.AmazonHttpClient$RequestExecutionBuilderImpl.execute(AmazonHttpClient.java:649)
    at com.amazonaws.http.AmazonHttpClient.execute(AmazonHttpClient.java:513)
    at com.amazonaws.services.securitytoken.AWSSecurityTokenServiceClient.doInvoke(AWSSecurityTokenServiceClient.java:1307)
    at com.amazonaws.services.securitytoken.AWSSecurityTokenServiceClient.invoke(AWSSecurityTokenServiceClient.java:1283)
    at com.amazonaws.services.securitytoken.AWSSecurityTokenServiceClient.executeAssumeRole(AWSSecurityTokenServiceClient.java:466)
    at com.amazonaws.services.securitytoken.AWSSecurityTokenServiceClient.assumeRole(AWSSecurityTokenServiceClient.java:442)

So if the third party AWS account want to do security audit to my account using his access key, how should it be correctly configured?

The error says that

arn:aws:iam::thirdparty:user/TestOne

is is not able to assume the role of interest.

In your question you correctly allowed the arn:aws:iam::thirdparty:root to assume the role. But this still is not giving TestOne IAM user permissions to do the same.

To fix that, the admin/root of the thirdparty account must explicitly allow IAM user TestOne to sts:AssumeRole in your account.

Thus the thirdparty account can add such permissions as inline policy to the TestOne user, for example. Obviously it can also be done using customer managed policies, or other IAM mechanisms. But inline policy seems as fastest and easiest to test.