This is not a speculative thread. Only facts and testimonies of one of the participants of the event. Some of rumors will also be described here just to give an integral picture
Tamerlane ("The Iron Lame")
Tamerlane was a 14th-century conqueror of West, South and Central Asia, and the founder of the Timurid dynasty in Central Asia, and great-great-grandfather of Babur, the founder of the Mughal Dynasty, which survived as the Mughal Empire in India until 1857.
The Empire of Timur
He triumphed over Golden Horde and Ottoman Empire. He destroyed Baghdad and Delhi. He besieged Moscow but then, for some unknown reason, took it off. The Russian Orthodox Church ascribes this miracle to the icon of Our Lady of Kazan, which, by the way, also came up in WW2.
An estimated 17 million people may have died from Timur's conquests.
The Tomb of Tamerlane
Tamerlane and his descendants were buried in the mausoleum Guri-Amir in Samarkand, the capital of the Timur Empire. The epitaph on the Timur's gravestone warns against disturbing the spirit of the great conqueror. It prophesies that "
the greatest war will happen if the grave of Timur is open".
In 16th century the Shaybanids took power and moved the capital to Bukhara and Samarkand went into decline. After an assault by Persians, the city was abandoned in the 18th century. And the tomb of Timur was forgotten.
Guri-Amir in the beginning of XX century
Guri-Amir was reconstructed in the Soviet era (photo from my camera made in 2008

)
Tamerlane and Stalin
Probably due to Tamerlane's decision to leave Moscow in peace, he was praised by Stalin as a leader of the Resistance to the yoke of Mongols and the conqueror of the Golden Horde.
Dr. Gerasimov
Gerasimov (2 September 1907 – 21 July 1970) was an anthropologist who developed the first technique of forensic sculpture based on findings of anthropology, archaeology, paleontology, and forensic science. He studied the skulls and meticulously reconstructed the faces of more than 200 people, including Yaroslav the Wise, Ivan the Terrible, Friedrich Schiller, Rudaki and, most famously, Timur (Tamerlane).
Timur's face reconstructed by Gerasimov
Opening the Tomb
In June 1941 Stalin sent Gerasimov to Uzbekistan with a team of archaeologists to find and open the tombs of Tamerlane and other members of the Timurid Dynasty. The opening of the family tomb should be documented by a film crew.
There were discussions on the location of the tomb. Some scientists thought that it was in Shahrisabz, home city of Timur. The others believed that it was in Samarkand (Guri-Emir).
The team started its work in Samarkand and found some tombs in the basement of the Guri-Emir.
First they opened the grave that supposedly held the remains of Ulugbek (the grandson of Timur and famous astronomer). The cleaved jugular vertebrae proved that the skeleton belonged to Ulugbek, who was beheaded by the order of his son.
The stone on the Timur's grave was broken. This fact corresponded with one legend. Persian King Nader Shah, who idolized Timur, took his gravestone as a trophy after the capture of Samarkand. After that, misfortunes one by one started haunting Nader Shah, and he was advised to bring the gravestone back. However, during the trip it was broken.
Thus, Gerasimov's team proved that they found the family tomb of Timurids.
The gravestone
Mystic facts
1. The opening of the Timur's tomb was carried out early morning in June 22, 1941. It coincided with Hitler's attack against the Soviet Union. In results of the war the USSR lost 26.6 million men and women in total, more than any other country in human history.
2. Timur's remain was returned to the Gur-e Amir Mausoleum under full Islamic burial procedure in November 1942, the Red Army launched Operation Uranus successfully in Stalingrad, which was the turning point on the Eastern Front.
The testimonies of Malik Kayumov Malik Kayumov (1911-2010) was a cameraman in the Gerasimov's team.
1. Due to numerous and unexplainable problems the film group failed to shoot the process.
2. Malik Kayumov and the other member of the team Ayni met three old men that warned them against opening the tomb and showed them the book that prophesied the catastrophe. Ayni insulted the old men and drove them away.
3. Malik Kayumov served in the Red Army as a military cameraman and many times he tried to meet high-ranking officials to tell this story. He managed to meet Zhukov in 1942 and asked to inform Stalin. Soon Timur's remains were reburied in Samarkand.
The rumors
The aircraft transporting the Timur's remains from Moscow back to Samarkand made a big detour and flew over Stalingrad.
There are similar rumors stating that in 1941, when Wehrmacht approached to Moscow, Stalin ordered one pilot to take the icon of "Our Lady of Kazan" (that very icon that protected Moscow from Tamerlane) and fly around Moscow.