Yes, that is exactly how it works. The number you received is a local phone line that forwards directly to the phone number you provided when you signed up. When your inmate dials it, the call routes straight to you.
Before that first call can happen, there is one step that needs to be completed on the facility's end. Your inmate needs to register the new number through the prison's phone system. In the federal system that means submitting it to their counselor or unit team manager for approval. In state facilities the process is similar but may go through a different person or department. Either way, the inmate handles that step from inside.
Once the number is approved, your inmate can dial it using their commissary funds or whatever calling account is set up at the facility. The call goes through the prison's phone system the same way any other approved call would, except instead of paying long-distance rates they are dialing a local number. That is where the savings show up, and once you see the difference in the per-call cost compared to what you were paying before it becomes very clear why the service is worth it.
To summarize the two things that need to happen before the first call:
After that it is straightforward every time.
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