The good news is that in most state systems the approved call list travels with the inmate rather than being wiped and rebuilt from scratch at each new facility. The list is tied to the inmate's DOC number rather than to a specific location, which means your number should still be on there when they arrive at the new facility.
The gap in calls after a transfer is almost always about logistics rather than the list itself. When an inmate arrives at a new facility they go through an intake process that includes housing assignment, orientation, and getting settled into the unit's routine. Phone access typically becomes available once that intake process is complete and they have been assigned to a permanent housing unit rather than a temporary holding area. Depending on the facility and how smoothly intake moves, that window can be anywhere from a few days to a couple of weeks.
Once they are in their assigned unit and have access to the phone system, calls should resume using the same approved numbers from before the transfer. If your number was on the list at the previous facility it should work at the new one without any additional steps on your end.
If calls do not come through within two weeks of the transfer, it is worth having your inmate check with their new unit officer to confirm the call list transferred correctly. Occasionally there are data issues where a list does not carry over properly, and a quick inquiry to unit staff can get it corrected without a lengthy wait.
In the meantime, letters through InmateAid are the most reliable way to stay connected during the transition period before phone access is reestablished.