The brief
The A3 had its ABS warning light on, on and staying on. He brought it in to get the system back online. When the ABS light comes on, the most common cause is a faulty wheel speed sensor. Each wheel has a small sensor that reads how fast it's turning, and the ABS uses those readings to know if a wheel is about to lock under braking. When one of those sensors fails, the ABS can't trust its picture of the road, so it puts up the warning and steps back, leaving you with ordinary brakes that work fine but without the anti-lock function. A failed sensor doesn't recover, so it needs the sensor changed.
The diagnosis
On the scanner the codes pointed cleanly at one wheel speed sensor, its signal dropping out, and a meter check at the connector confirmed the sensor itself was the failed component, with the harness and the tone ring it reads off both fine. That's a sensor replacement. A failed wheel speed sensor doesn't come back, so the sensor was getting changed.
The work
The car went up, the failed wheel speed sensor was unbolted from the hub and a new genuine Audi-spec sensor fitted with a fresh O-ring, the harness clipped back into its proper run so nothing rubs. Then the stored faults were cleared from the ABS module and the system checked over. A road test with a series of braking events confirmed the warning stayed off and nothing came back.
The outcome
ABS warning off, the anti-lock system back online, and no codes after a drive cycle. The A3 went home with the braking electronics working properly again. The ABS is there for the moment you need it, so getting the failed sensor changed and the system reset put the safety net back where it should be.