SMS text messaging for FB lives
For stores on our SMS plan or above, you can enable an automatic text message whenever your live starts.
You can edit the SMS message that goes out in your Settings tab:

We limit this message to 100 characters since we need room for the FB Live URL as well as the opt-out text (required for compliance).
We strongly recommend collecting phone numbers at your Shopify checkout so that you can build up your SMS subscribers. This article from Shopify guides you on how to collect customer phone numbers.
More details on SMS text messaging:
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We prevent stores from sending SMS more than once every 12 hours. So if you do 2 lives within 12 hours of each other, only the first live will send out SMS texts to your customers
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If you have more customer phone numbers than the SMS quota that your plan allows, we send SMS texts to the most recent customers.