Welcome.
Seen the online services that allow you to send free SMS to mobile numbers using Google Calendar API.
But I couldn't find such an implementation that would allow to send a very small amount of SMS when you receive mail to the address — irrespective of the operator using, for example, Google Calendar.
Not seen such an accident?
PS Guess what to write for himself would have been easy, but, alas, not a programmer, and commercial interest there — you just need to periodically get notifications about important events on the telephone.