Yes, he should be able to keep the tablet. Since he is moving within the same Florida Department of Corrections system rather than crossing into a different corrections network, the tablet he purchased through JPay travels with him as his personal property. DOC facilities operate under the same umbrella, which means the tablet and the JPay account associated with it remain valid at the new facility.
That said, there can be a gap in access immediately after a transfer. New arrivals typically go through an intake process at the receiving facility before they are fully integrated into the housing unit and have regular access to their belongings and electronics. During that window, which can last anywhere from a few days to a couple of weeks depending on the facility's intake procedures, the tablet may be held with his other property until he clears intake and gets settled into his permanent housing assignment.
Once he is through intake and in his assigned unit, JPay messaging, music, and any other content on the tablet should resume normally. His JPay account is tied to his DOC number rather than to a specific facility, so the contacts, messages, and content he had at Lawtey will be there when he logs back in.
If more than two weeks pass after the transfer and he still does not have access to the tablet, he should put in a written request to the property officer at the new facility asking about the status of his personal electronics. Keep copies of any requests he submits.
In the meantime, sending letters through InmateAid is a reliable way to stay connected during the gap before JPay access is restored.