AZ 610 then DL 1859 at JFK
Rome → New York → San Juan
Timetable, New York time
18:55AZ 610 from Rome at the gate
18:53DL 1859 to San Juan leaves the gate
23 h 58 apart on the timetable, overnight
DL 1859 leaves 23 h 58 after AZ 610 arrives on the timetable: more than half a day, so not a connection we count.