Possible to add Conversation Id to email subject? Or otherwise associate email replies with existing Salesforce cases?

Hi! We’re trying to resolve an inconvenience in our Salesforce org where if a customer replies to an Intercom conversation via email, their response creates a new case in Salesforce instead of getting added to the existing case. I could set up a flow in Salesforce to associate these new email responses to their existing case if we could get the conversation Id into the email subject. Is there a way to do this? Or has anyone else found a better way to tackle this in Intercom/Salesforce?