You're mistaken, this problem has already been solved as 10 seconds of Google-Fu have revealed.

Could you share the insights of your research? I only found solution involving the Google API (as it was also discussed here some days ago).

https://startpage.com/do/search?query=ssh+two+factor+sms turns up Authy as the first hit.

You could use privacyIDEA, which is a two factor auth server and is also capable of sending SMS via HTTP gateways.

BUT: You would rather want to use 2nd factors like HOTP or TOTP token or a yubikey.

SMS isn't particularly secure. It's a little disturbing that some people use it for authentication.

Please tell my bank :)

If you have an iphone it will even sync it back to your Mac for you :D

TOTP is superior, no chance of social engineering your phone company to redirect the messages.