The brief
The A4's air conditioning had a problem at the source: the airflow from the vents was weak, stuttering at some fan speeds and dropping out at others, with a noise from behind the dash. He brought it in. That's the blower fan, the motor and fan that push the cooled air into the cabin. The motor's bearings wear and get noisy, the fan can foul on debris, and the speed control can go flaky, so the airflow drops off and stutters and the fan rattles or whines. When the blower's reached that state you replace the fan motor assembly, fitting a fresh unit rather than chasing a worn one that's only going to keep deteriorating.
The diagnosis
A check confirmed it, the blower fan motor was worn, drawing badly and noisy, the airflow weak and inconsistent because the fan wasn't spinning up properly. The ducting, the cabin filter and the aircon controls checked out, it was the blower unit itself. That's a blower motor replacement, you don't rebuild it on the car, so the call was a complete blower fan assembly, fitted and tested across the speeds.
The work
The trim and the bits in the way came off to reach the blower, the failed unit unbolted and removed, and a new genuine Audi-spec blower fan assembly fitted, connected up, the ducting checked clear, the cabin filter checked, and the trim refitted. The blower was run through its full speed range to confirm it spun up cleanly and pushed proper airflow. A check confirmed strong, steady airflow from the vents at every fan speed, with no stutter and no noise.
The outcome
Strong, steady airflow from the vents at every fan speed, no stutter, no noise, and the cabin cooling properly again. The A4 went home with the airflow sorted. A worn blower only gets weaker and noisier, so changing the assembly put the aircon airflow back where it should be.