Where I work, we use Pushover (https://pushover.net/) for this. A message comes in via SMS and then a handler stores it in a database then turns around, does some light filtering[0], and then sends a notification to a Pushover group. It's $5 per user per month for their teams feature, which we happily use.

0 - The handler doesn't send out via Pushover any message that contains words we're unlikely to use; Facebook is one, for example. If a message isn't forwarded via push notification, it is emailed to the sysadmin list for one of us to manually look at during daytime hours.