The facility is not going to deliver that message for you through official channels. Staff are not supposed to pass phone numbers from outside parties to inmates, and while an occasional empathetic officer might make an exception, that is not something you can count on or plan around.
The two reliable options are mail and visitation.
Mail is the most straightforward. Write the new number in a letter or on a postcard and send it directly to your inmate at Fayette County. InmateAid can handle that for you through the letter service, or you can mail it yourself. Either way it will arrive through normal mail delivery within a few days and your inmate will have the number in hand.
If you have a scheduled visit coming up, handing them the number in person during visitation is the fastest option. They can write it down and submit it to the phone carrier to be added to their approved call list right away.
Once they have the number the next step is on their end. They will need to submit the InmateAid number through whatever process Fayette County uses for adding numbers to the approved call list, whether that is through a kiosk, a form submitted to staff, or directly through the phone carrier's system. That approval typically takes a few days to process before the first call can come through.
If you want to confirm the number is active on InmateAid's end before you send it, reach out to aid@inmateaid.com to verify the account status first.