Setup elastic email as trusted sender

We are using Elastic eMail as mailing provider. Emails sent from one of our domain accounts to another are bouncing (i.e. [email protected] to [email protected]). Elastic eMail tells us this is because these emails, although internal, are handled externally by their servers, and our server is not recognizing Elastic eMail as a trusted sender. They say: "To prevent this, please check with your provider what you need to do to use Elastic Email as authenticated sender". Please advise what we need to do to use Elastic Email as authenticated sender. Thanks.