AA 2768 then DL 1859 at JFK
Phoenix → New York → San Juan
Timetable, New York time
19:00AA 2768 from Phoenix at the gate
18:53DL 1859 to San Juan leaves the gate
23 h 53 apart on the timetable, overnight
DL 1859 leaves 23 h 53 after AA 2768 arrives on the timetable: more than half a day, so not a connection we count.