To her friends, Hilde Back was a quiet, elderly Jewish woman who used to teach pre-school children and had lived alone for 35 years. But to Chris MBuru she was "an angel who had walked into my life and fixed it".

Back, now 88, is the star of Jennifer Arnold's new documentary, A Small Act, after she unwittingly inspired the largest educational fund in Kenya.

"I think there's so much need in the world that we need to help. It just felt normal to donate some money to a child," she says.

"What you send is just a drop in the ocean. I don't have much, and sometimes you wonder whether it helps."

In the mid '70s, she decided to send about £10 a week to a young, rural Kenyan boy. In Chris MBuru's region of Kenya, most women give birth at the age of 15 and, although secondary school costs less than half the money Hilde provided, most families still cannot afford to educate their children. "She didn't just give me money, she gave me hope," MBuru says.

Back's weekly £10 allowed MBuru to stay on at school rather than work the fields with his family. He grew up in a mud house and studied by candlelight. He ended up graduating from Harvard law school and now works as a human rights investigator for the United Nations.

Inspired by this stranger's generosity, MBuru started a scholarship programme and named it after his benefactor - The Hilde Back Educational Fund - before deciding to find the startled woman "who made my life possible".

MBuru tracked Back down to her home in Sweden and brought her to his small, poverty-stricken village. She was greeted by the entire population and made an honorary elder. She was completely unaware of the difference her donation had made. Her arrival, recorded in grainy footage on a '90s camcorder, she looks completely overwhelmed.

"When I first met her, I was amazed by her simplicity," MBuru says. "I always assumed she was a wealthy woman looking for ways to spend her money. It turns out that she was an ordinary person with a normal life, and that really struck me - that she didn't realise she had done anything important. She didn't see herself as a hero, but she is my idea of the world's grandmother." From its origins in MBuru's village, the Hilde Back Fund now provides money for projects across Kenya.

Arnold's documentary about the story of Back and Mburu is governed by this simple idea - that the smallest gestures of kindness can ripple out to make the most extraordinary difference.

Indeed, as Arnold discovered during the shoot, Back's own survival was based on a small act of kindness. Back is not a native Swede. She arrived from Germany in 1940 after a stranger gave her and her parents enough money to escape persecution from the Nazi regime.

Fleeing across the Baltic Sea, her parents tried to enter Swedish border but were rejected at the border. As a child, Hilde was allowed in. "We thought maybe we could see each other later," Back says. "But we didn't."

Returning to Germany, Back's mother was sent to Theresienstadt. Her father to Auschwitz.

"I think it's very important to care about other people from other cultures," Back says. "I was once helped to escape the Nazis and come to Sweden, and it can affect you very much. I think it has affected me."

It is a subject she had kept private until Arnold approached her with the idea for the film. Back reveals a hidden photo-album with a few black-and-white images of her life as a Jewish child in pre-war Germany. One shows her playing with a Nazi flag.

"When I started looking at the pictures I became distraught and thought: 'How the heck could we have played with such things when we were Jewish children?' But I think it's simple. All children do as other children," she says.

"When I first wanted to tell the story I was really struck by the parallel of the fact that Chris works in human rights and Hilde was a Holocaust survivor," Arnold says. "I knew she had never really talked about her experience of the Holocaust before I started making the film and we weren't entirely sure whether she could open up about it, so in the first initial interviews we were testing the waters, but actually she was quite happy to talk about it.

"She said she hadn't talked about it before, but she went into a lot of detail, and I hope it was something that was cathartic for her."

"I feel it's like something woven into one from two different pieces," MBuru says. "I'm a religious person, I believe in a great protector. I felt as a child I was in the hands of fate, but I felt that if times were hard, things would be all right if times were hard because someone would come and help me, and that turned out to be the case."

Back first saw A Small Act at its premiere at the Sundance Film Festival in the United States last year. During the second screening a woman stood up in the audience and offered a $5,000 donation to the Fund. She challenged the audience to give, too, and her $5,000 was quickly matched by another audience member. Over the 10 days of the festival, the amount pledged had grown to $90,000. "Hilde, was literally walking out of screenings with money stuffed into her pockets," Arnold says.

"The film has changed all our lives, but I think it has given Hilde this tremendous third act to her life that she wasn't expecting," says Arnold. "It's unusual to discover fame at 88."

But what does the fund intend to do with this sudden influx of money?

"We want to expand," MBuru says. "When I first met Hilde, we were sponsoring 10 children. Last year we took on 60 new kids. This year we are taking on 160."

At a United Nations event in New York recently, General Secretary Ban Ki-Moon praised the film "for highlighting the importance of giving all children an education in the fight against ignorance and bigotry."

"Education in a lot of third world countries is sometimes perceived as a privilege, but in fact it is a right," MBuru says.

"It is a duty, and we want to send the message that the responsibility does not lie with the charities but lies with government. The charities are stepping in because government has failed. The issue of education lies at the heart of development. If you are not educated, you are vulnerable.

"Meeting Hilde and finding out about her past has reinforced this commitment. It has only strengthened my belief."

'A Small Act' is currently showing in cinemas nationwide. For more information on the Hilde Back Education Fund, visit www.hildebackeducationfund.com

Hilde Back Education Fund