When Williams pulled the car over last month the woman gave false details and was arrested.
It emerged she had been disqualified from driving eight years earlier and had never tried to requalify because she was embarrassed by her problems reading and writing.
"I phoned NZ Transport Agency and confirmed what she had to do to obtain her licence," Williams said.
"She didn't know you could have a reader at the test. I offered to be hers."
Williams then recommended an app and the woman studied road theory with the help of her son.
A week later on January 31 she sat the test with the senior constable reading the questions.
"My shift was changed so I could get there," Williams said. "She failed with 31 out of 35 - you're only allowed to get three wrong. She had clearly studied, though, as the mistakes were silly ones.
"She couldn't afford to pay for the test again so I paid for a second go. I thought if we don't do it now it'll go into the too-hard basket. Second time she passed with room to spare."
Williams then took the woman to the Hamilton Central Police Station and helped her with appeal forms for the return of her impounded vehicle.
The woman, who had been before the courts in the past, still faces charges of driving while forbidden and giving false details.
"I hope this positive experience of police will help her see us as 'not the problem' and that she'll continue to take the right steps," Williams said.
Although the case might appear trivial compared to other police work, Williams said it was about making a difference.
"If we can't invest a little time and effort in people, what hope is there for them?"
The woman said through police she has now booked the practical part of the requalification test for next week.
"He was so cool," she said of Williams. "I'm so thankful to him. I gave him a big hug and there were a couple of tears."
Williams' supervisor, Acting Sergeant Will Hamilton, said the episode was "the perfect demonstration of the essence and spirit" of police work.
"Senior Constable Williams has set the bar for going the extra mile and delivering the outcomes we all strive for," he said.
"I'm proud of and him and will continue to enable and support him to produce positive outcomes like this."