Working for them was a 25-year-old interpreter called Yelena Rzhevskaya, the Daily Mail reported.
As her regular role involved interrogating captured Germans, she might have thought when she was summoned that afternoon to the office of her commander, Colonel Gorbushin, that she was going to be wheedling some intelligence out of a Nazi.
"It was a second-hand, burgundy box with a soft lining and covered with satin," Yelena later recalled.
She asked Gorbushin what it contained. His matter-of-fact reply startled her. 'Hitler's teeth,' he said. 'And if you lose them, you'll be answerable with your head.'
What followed remains one of the strangest missions of the entire Second World War.
Although German radio had announced that the Nazi leader had killed himself eight days before, on April 30, 1945, confirmation was needed urgently.
Many suspected the Fuhrer could have escaped from Berlin and was either hiding somewhere in the Bavarian Alps, or even under the waves of the Atlantic in a submarine en route to South America.
The task faced by Yelena's unit was to see whether the charred teeth discovered in the grounds of the Reich Chancellery really did belong to Hitler.
Today, thanks to the long-awaited publication of Yelena's memoirs in English, the world can finally learn the true story of how the Russians confirmed the Fuhrer's death.
Her memoirs will hopefully dismantle the increasingly popular conspiracy theory that claims Hitler did indeed survive the war…
So why was Yelena chosen for this historic task? That was the first question she asked as she opened the satin box to find a charred fragment of lower jaw and some dentures.
"Because we have no safe here," replied, Colonel Gorbushin, "and as a woman, you're less likely than a man to get drunk and then lose them."
Yelena was almost overawed by her new responsibility, and later admitted that she turned cold whenever she worried about losing the box.
Her first objective was to track down Hitler's dentist – no easy task in the chaos of the war-torn German capital.
With their driver Sergei behind the wheel of a Ford 8 saloon, she and her two officers headed into the centre of Berlin.
"In places smoke was still rising, the city's air still filled with the fumes of battle," she wrote.
"The barricades, crushed by tank tracks, had yet to be dismantled." After many hours, the team pulled up at a hospital, and enquiries were made about who had looked after Hitler's teeth.
The doctor in charge did not know, and the only name he was able to supply of those who had treated Hitler was that of the internationally renowned laryngologist Professor Carl von Eicken, who headed the Charite clinic.
It was the only lead they had, and later that day, the team arrived at the clinic. It was a grim place, covered in camouflage stripes to supposedly guard against aerial attacks.
The ear, nose and throat department was located in the basement.
"Nurses in grey, with white head-scarves bearing a red cross, looked exhausted as, sternly and silently, they went about their duties," Yelena recalled.
"Wounded patients were being carried on stretchers."
The elderly figure of Prof von Eicken emerged, and told the Russians he did not know the identity of Hitler's dentist, but somebody from the dentistry department might.
A student was summoned, and he revealed that the dentist was called Dr Hugo Blaschke, and he could show the Russians where he worked.
The dentist's surgery was located on Kurfurstendamm, one of Berlin's most fashionable streets.
It was largely a ruin, but somehow Blaschke's building had survived. However, almost as soon as the team arrived, it looked like they had reached a dead-end.
A man called Dr Bruck informed them that Dr Blaschke had flown from Berlin to Bavaria. Nevertheless, the team looked around the surgery, until Col Gorbushin asked if Dr Bruck was in contact with any of Blaschke's employees.
"Of course!" Dr Bruck exclaimed. "You mean Kathchen? Kathe Heusermann? She is at home in her apartment right on our doorstep."
Within a few minutes, an attractive woman in a dark blue flared coat came in. She was wearing a headscarf over luxuriant blonde hair.
"Kathchen," said Bruck, "these people are Russians. They seem to need you for something." Heusermann burst into tears, fearing she was going to be raped.
Like so many other women in Berlin, she had already been violated by the troops of the Red Army. However, Dr Bruck was able to reassure her that this group of Russians meant her no harm.
Heusermann revealed that she was 35, and that her fiance had been a teacher and now, as a non-commissioned officer, was somewhere in Norway and she had heard nothing from him for a long time.
Dr Blaschke had invited her to be evacuated with him, but she refused.
Col Gorbushin told Yelena to ask her whether they had Hitler's dental records. Heusermann said they had, and immediately took out a box with record cards.
'We watched with bated breath as she flicked through them,' Yelena wrote in her memoirs. 'We glimpsed the cards of Himmler, Goebbels, his wife, all their children… At last Hitler's medical card was found, and that was a start, but there were no X-rays.'
Heusermann suggested they might be in Blaschke's other surgery – in the Reich Chancellery itself. Once the very heart of the Third Reich, the Chancellery on Wilhelmstrasse had suffered the ravages of war.
The team walked through the entrance, where above them, in bas-relief, was the Nazi emblem: a spread-eagle clutching a swastika in its talons.
Heusermann led the team to a little room. The torch dimly illuminated a dentist's chair, a couch with an adjustable head-rest, and a small desk.
After searching through a cabinet, the team found X-rays of Hitler's teeth and his dental records.
The following day at 10am, the Russian officers sat down with Heusermann and asked her to describe Hitler's teeth from memory.
Yelena was translating and making notes, and specifically asked Heusermann not to use the technical names for the teeth, in case there was a confusion in the translation, but instead simply to number them.
'Hitler's upper denture was a gold bridge attached to the 1st left tooth with a window crown, to the root of the 2nd left tooth, to the root of the 1st right tooth and to the 3rd right tooth with a gold crown…'
The team compared Heusermann's words with the X-rays.
Crucially, they matched. But more importantly, did they match the remains contained in the burgundy box? Yelena passed the teeth to Heusermann, who held them in her trembling hands.
She took a deep breath, then blurted out: "These are the teeth of Adolf Hitler."
For Yelena and the team, this was incontrovertible evidence. 'I really believed that all the nonsensical rumours that Hitler was alive would be swept away and truth would prevail,' she wrote.
Yelena was certain the team would soon be sent to Moscow with the evidence and principal witnesses to the identification of Hitler's remains.
But then something strange happened – or rather nothing happened. Because what took place, in the ruins of Berlin in May 1945, was a cover-up, personally ordered by Stalin, to keep the world guessing.
So what happened to Hitler's teeth? Yelena last saw them in Berlin in late May 1945, when they were being placed in a special container to be sent back to Moscow.
After that it was not known for certain whether they still existed.
However, in 2000 the Russian authorities put the teeth on display as part of an exhibition to celebrate the 55th anniversary of the end of the Second World War.
After the war, Yelena returned to Moscow and became a writer. She died in April last year, after only discovering in 1996 what had happened to Kathe Heusermann.
"I know that if we had not found Kathe, Stalin's plan would most likely have been successful and Hitler, as Stalin wanted, would have remained a myth and a mystery," she wrote.