Can we be notified when civi recieves an SMS?
Lisa, Welcome to CiviCRM SE. Since Civi stores response as a activity, you can create schedule reminders to send sms/email for Activity type 'Inbound SMS' with 0 hrs after activity date time and limit to group of contacts. You can also use tokens like activity details, contact name etc in your message.

Using CiviRules extension you can send email/sms by using trigger 'Activity Added' with Filter 'Activity type' as 'Inbound SMS' and Action as Send SMS/Email. (You will need to Install CiviRules extension along with Email Api extension to send email or SMS api extension to send sms)

HTH

Pradeep