To send an Email to SMS using subject authentication instead of allowed senders, send an email with the subject line containing the following format:
auth~{HTTP_API_USERNAME}:{HTTP_API_PASSWORD}~Email Subject
Insert your SMS content into the body of the email.
The HTTP API username and HTTP API password can be found in the API Integrations page located here under 'Master API Keys'.
Any replies to Email to SMS sent via this method will behave the same way as using allowed senders, which can be seen here.
Note: ~Email Subject portion is optional and does not need to be included.