Hello ​@PluckyDad ,
There isn't a native feature for this, but it's entirely possible to create a step that does exactly what you're looking for.

If you're using ManyChat's AI, you can try adding an extra task within the AI step to save a summary of the conversation in a custom field.

Of course, some testing will be needed — it's unlikely you'll be able to save the entire conversation, but I believe a summary is feasible.

After completing the AI step, you can add an email block to send the saved summary to yourself.

Thanks Rogerio!