I just built a similar feature into our app, where our users may specify email contacts and send chat messages to them. Those messages will be sent using a special email address containing our user ID, so we can route responses back into our chat database. By storing the email message IDs along with the messages, we can even implement full conversations and let our users and external recipients respond to specific messages.
This was rather cheaply possible using Mailgun webhooks - we even have delivery receipts!<p>Edit: in case somebody worries - this is a B2B application where buyers can talk to their suppliers, some of which may not be onboarded yet. We rate limit sending out too, so there’s not really a spam risk :)