I offer you a shortcut that allows you to use the export function of My Groups to send an SMS message to the members of a contact group.
Download this shortcut from your iPhone or iPad, then follow the instructions to add it to your list of shortcuts.
Note: This shortcut is compatible with the iOS 13 version.
You might encounter an error from Shortcuts when trying to install this shortcut.
This is because on iOS, you are not allowed, by default, to install a shortcut from untrusted sources.
To fix this issue you shall open the Settings app:
- go to the Shortcuts section;
- check the option “Allow Untrusted Shortcuts”
This is explained in a how-to from Apple.