One spring day in 2002, a French woman whose name we may never know, stood on a cross-Channel ferry and threw a bundle of clothes into the sea. After it, went some lilies and a bottle in the shape of a teardrop. The clothes had belonged to her son, Maurice, who had died at the age of 13, and the bottle held her letter to the boy "that no wind … no storm … not even death could ever destroy".

"Forgive me for being so angry at your disappearance," the letter went. "I still think there's been some mistake, and I keep waiting for God to fix it … Forgive me for not having known how to protect you from death. Forgive me for not having been able to find the words at that terrible moment when you slipped through my fingers … "

The bottle vanished, the ship docked, the mourner went home to get on with her life. She never dreamed the letter would reach shore, let alone that someone would read it.

Karen Liebreich, a London-based author, did just that a few weeks later. The bottle had washed up on a beach in Kent, where it caught the eye of her friend Sioux Peto, who was walking her dogs. Inside, Peto found a thin scroll tied with a ribbon and enclosing a lock of hair. The handwriting was in French and, as Liebreich is fluent in the language, Peto sent her the letter for translation.

This was tougher than it might have been, with the anonymous writer addressing now her son, now an imagined reader, and piling watery image upon watery image. "You can't just skim it and understand it," Liebreich says.

As far as she could tell, the boy had died early one summer, probably by drowning. "For a long time," his mother wrote, "he travelled between two waters, between two lights, trying tirelessly to use up the strength in his outstretched arms. He submitted to the silence, the terrors and the cold … "

She had, of course, been devastated – "My life started when he was born, and I thought it was over when he left me" – and for a while Liebreich was afraid she might be reading a suicide note. But no, the woman was ready to move on. "While God gives me life," she wrote, "I promise you to live it to the full, to savour each instant in richness and serenity. I know that we will find one another, when the time comes."

As she translated, Liebreich found herself crying. "I'm not a weepy person," she says, "but the letter was very beautiful and very moving."

Liebreich couldn't sleep that night. In the days that followed, she found herself becoming more protective of her own children – Sam, then 10, and Hannah, eight – even, perhaps, of her husband, who is a doctor. "When your children are young, you can get lost in all the banality," she says. "The house is full of toys and laundry and stuff from school, and in the boredom of the domestic routine you forget how precious they are. Something like this reminds you how important they are."

Still, that could have been the end of the affair. Liebreich might have dried her tears, regained her rhythm and only occasionally thought of the woman whose story had shaken her. Instead, she set out to find her. "I was plagued by unworthy emotions," she explains in the book she subsequently wrote about the search. "I wanted to know how Maurice had died; I wanted to know what his mother was like; I wanted to know whether I could track the origin of an unsigned letter in a bottle. I wanted the writer to know that the bottle had been found on an English shore and that I had read her letter. I wanted to reassure myself that she was all right."

Did the woman want to be found? Wouldn't that just rake up all that pain again? "Sending a letter in a bottle invites a stranger to pick it up and read it," Liebreich told herself. "I think the unknown mother wanted the tale of her love for her son, the knowledge of his death and her despair, to be known."

Liebreich has experience as an investigator, having tracked down old Nazis for the BBC series Timewatch and a previous generation of paedophile priests for her book Fallen Order. The only things she knew for sure, however, were Maurice's first name, the age at which he died, that he was his mother's first son, and the name of one of her friends, Christine, described in the letter as "gentleness itself". And she soon discovered that much of this knowledge was useless, with France recording deaths not in one central register but in 36,000 local ones. There was no hint of foul play, so no reason for the police to get involved.

Over the next few years, Liebreich consulted newspapers, bottle-makers, sailors, doctors, graphologists, psychologists, psychotherapists, secret servicemen, literature professors, forensic scientists, private detectives, even clairvoyants and tarot readers. "The letter would not leave me in peace," Liebreich writes. "But each time I considered giving up I thought I would make one more effort – one more email, one more phone call, one more visit to the library. The answer might be round the next corner."

Experts provided various explanations. The boy had indeed drowned, said one. Water was not involved, said another. He might have overdosed on ecstasy, said a third. The mother and child were close. Unhealthily close. Estranged. The letter had been thrown from a cliff. No, a boat. The woman was dead. No, she was a survivor. She was definitely a lesbian, unless of course she wasn't.

When others weren't feeding her red herrings, Liebreich was doing it herself. "The fact that the letter was so opaque meant that I went off on tangents," she admits. It took her six months to realise that perhaps Maurice hadn't drowned at all, and the letter's "water", "harbour", "vessel" and so on were nothing but metaphors. It never occurred to her that his death "at the dawn of summer" might have referred to his age rather than the calendar.

After three years, Liebreich decided enough was enough. If she couldn't find Maurice's mother, she could at least write about the search. "If, somewhere, the letter-writer is alive," her book concludes, "then perhaps this book can serve as a clumsy 'letter-in-a-bottle' reply … I wonder if she will receive my message."

She did. In 2009, three years after The Letter in the Bottle came out in Britain, the nameless "she" got in touch to say she felt violated. As she put it, it was as though her story, her suffering, her very intimate being no longer belonged to her.

By then, the book had been published in French, to huge media coverage. "In Britain the story was seen as a failed quest," Liebreich recalls. "In France it was an unsolved mystery." Years before, she had struggled to interest the media; now she was worried that Maurice's mother would be outed by a friend or neighbour. Instead, the mother contacted Liebreich via the psychologist Olivier Roussel, who runs the website unebouteillealamer.com - A Bottle in the Sea. She apparently saw him as one of the few sympathetic voices in the book. She might be willing to talk to Liebreich directly, but she needed time.

The author, who had no intention of upsetting her any more, gave her time. Readers wrote with tips for finding the woman or stories of their own losses. One Swiss man emailed that she should be ashamed of herself: she was hunting the mother like prey. Perhaps he was right, she thought.

The two women finally met a month later, in a nameless town in northern France. "She was very pretty, slim and elegant," Liebreich writes in the new, updated version of her book, "with a delicate face and good cheekbones … Though she later told me she was 60, she looked much younger … After searching for so many years, I could not believe I was there, face to face with the author of the letter. And so we talked."

Largely, it seems, about the many things Liebreich and her helpers had got wrong. Maurice had not drowned, but been knocked off his bicycle. He had died in 1981, 21 years before the letter was written, not just a few. The "dawn of summer"? "Just a lyrical expression." The talk of rupture, alienation, conflicts? "I was never in conflict with my son at all." The claim that they had lived together "almost as a couple"? "A shocking thing to say." The lesbianism? She had had a good laugh over that – probably one of her few while reading the book. And the medium's claim: "I don't think you will ever find her … she is no longer alive." "Well, I am alive and you have found me."

One false trail was laid by the woman herself – but she has paid the price for that. The letter's first draft had described Maurice as "the only person in the world (with my other sons) that I was born to love for ever". Somehow she omitted that nod to Maurice's three brothers while writing out the fair copy. It was not deliberate; it was not because she didn't love them. "The reason she didn't kill herself was the other children," Liebreich says. "She is their mother as well." It still took some explaining.

But what about Liebreich's own belief that the writer wanted to be found? "It never occurred to me that anyone would find my letter in the bottle," the woman explains in a postscript to the new edition. "I thought it would smash in the waves and the fragments of glass and paper would gently disperse through the oceans. I gave it to the sea, to the universe: it was perhaps my way of talking to God."

Maurice's mother, who Liebreich has promised never to name, seems to have forgiven her for reopening old wounds. "It was a terrible shock that it all came out," says Liebreich. "But I think she felt it was done sensitively. That was a great relief."

They have met again and may even be on the way to becoming friends. "We have found other things to talk about," Liebreich says. "We email each other. I think there's a friendship evolving that's not linked totally to this book and the death of the child."

"I still have the bottle," she adds. "We don't know what to do with it."

The Letter in the Bottle is published by Atlantic Books, £7.99. To order a copy for £7.49 with free UK p&p go to guardian/bookshop or call 0330 333 6846