Hi @Erin O'Brien,
Welcome to Microsoft Q&A forum.
Thank you for reaching out and sharing information regarding a user cannot post an event to a shared calendar and the other one with Microsoft 365 subscription is recognized as an external user of the organization.
To move forward securely, please check the private message session I have initiated with PII related:
- In your thread, you will see a banner regarding ongoing private message.
- Click View messages.
Thank you for your patience and cooperation. I'm looking forward to your reply.