When creating an event on a cPanel hosted calendar via iPhone or iOS, the "Invite" option does not appear.
cPanel makes use of the Horde calendar server by default. The Horde calendar server does not support the "Invite" option when used on iOS.
cPanel has introduced a plugin that is compatible with the "Invite" option on iOS called Calendar and Contacts Server which you may consider using instead of the default.
Install the Contacts and Calendars Server Plugin according to our documentation:
cPanel Docs - Install the Calendar and Contacts Server Plugin