Hi @oly ,
As far as I think,I suggest you could use Twilio to send SMS messages from your .NET Framework application.
More details,you could refer to below article:
https://www.twilio.com/docs/sms/tutorials/how-to-send-sms-messages-csharp#sign-up-for-or-log-in-to-your-twilio-account
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Best regards,
Yijing Sun