I would externalize this functionality with a REST service on my server.
Then, from iOS GO I would call the service using INSERT FROM URL passing whatever GET variables were necessary. (the service would also work with the browser, or Terminal, or any App that can do GET requests.).
Someone posted recently some information about Twillo.
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The most common way of doing this, is to use one of the sms service providers which allow you to send sms by email. You can send email directly from FileMaker without changing to the email client.