I am not sure what this is called, but I was a user on a Cisco system that had this feature. I want to my phone to automatically call an internal extension when internal extension hangs up. So I have the BLF set up on my phone for that extension. I see she is on it. I want my phone to automatically call as soon as she hangs up. What is this called, and can FreePBX 12 do it?
It’s called “callback”
https://wiki.freepbx.org/display/FPG/Callback+Module
But yes it only works for internal calls
(I see you have been around for three years, have you really never bothered to read the wiki a few times? 
)
I have read about callback and I am fairly sure this is not what I want. On the Cisco system, if you called the internal extension and it was busy, you just pressed a certain key (like *) and hung up. When the other person hangs up the phone, your phone rings, you pick up, and then it calls the other person.
My bad, sorry