You can create a webhook for this purpose. Whenever you will receive an SMS. Twilio will post details on this URL you have created and then you can parse this and write a script to send mail.
https://www.twilio.com/docs/glossary/what-is-a-webhook
https://support.twilio.com/hc/en-us/articles/223181788-Forwarding-SMS-Messages-to-your-Email-Inbox
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