I would like to know if there is a way users can be notified when a client replies to a text that has come from Civi. Our system is currently receiving SMS that have been sent to civi, but the only way of knowing they have been received is to look at each individuals activity list. I wondered if a notification to a user could be set up through Civi Rules? Has anyone been successful in setting this up? Thanks in advance.
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)