Notification is not sent to Record owner when an Incoming SMS is received.
•Incoming SMS owner is not assigned as the OAuth user (the user with whose access the incoming SMS is being pushed to the CRM)
•The related Contact/Lead/or any other record does not have the mobile number stored in recognized formats – (xxx) xxx-xxxx or 1xxxxxxxxxx (where “1” is the country code)
•The related record owner does not have access to the fields of incoming SMS object.
If the owner of the incoming SMS is added correctly and even then the owner does not receive a notification, check to ensure that the email notification is not being caught in the spam filters of the user’s Inbox.