If you're having difficulties using the @privaterelay.appleid.com email addresses you receive during Sign In With Apple, please consult the documentation that was just released which explains how to configure your sending email system to work with the privaterelay MTAs:
It is important to register your email sources as verified domains, subdomains, or individual email addresses for the privaterelay MTAs to identify your inbound email traffic as coming from your developer team. @privaterelay.appleid.com email addresses are currently not sharable between developer teams and will only work when sent from email sources registered to your team.
See the new section entitled "Authenticating Your Domains" for details.
Thank you for this!
We are now successfully sending emails through the relay service with SES.
I missed the registration of the "Individual Email Addresses".
All good now.