FR24 also works through multilateration, or MLAT, which is a method of triangulation by measuring the time it takes for the transponder transmissions to reach three or more receivers. It can give a rough position for an otherwise bearingless target. But it's not that accurate so you'll see things like C172s having a ground speed of 300 knots.
If a transponder hasn't got ES then it will need a radar interrogation before sending anything out. It'll then just be bearingless and show up as a ring, but it may not show up on the ground as it's not being illuminated by a radar down there.
Best option is to persuade the other person to get a PilotAware...