From the OCA website:
The Placing of the Precious Robe of Our Lord Jesus Christ at Moscow (1625): The Savior’s precious Robe [ Greek “himatia”, literally “over-garments”] is not identically the same thing as His seamless coat [Greek “khiton”, literally “under-garb tunic”]. They are clearly distinct within Holy Scripture. “Then the soldiers, when they had crucified Jesus, took His garments (ta himatia) and divided them into four parts, to every soldier a part, and the coat (kai ton khitona). Now the coat was without seam, woven whole from the top down. Therefore, they said among themselves, let us not tear it, but cast lots for it, whose it will become. Thus the saying in Scripture was fulfilled: they divided My raiment (ta imatia) among them, and upon My vesture (epi ton himatismon) did they cast lots” (John. 19: 23-24; Ps. 21 : 18-19).
According to the tradition of the Georgian Orthodox Church, the Chiton of the Lord was carried by the Hebrew rabbi Elioz from Jerusalem to Mtsket and at present is beneath a crypt in the foundations of the Mtsket Patriarchal cathedral of Svetitskhoveli (the Feast in honor of the Chiton of the Lord is celebrated on October 1). None of the Mohammedan invaders ever ventured to encroach upon this spot, glorified with a sign by the mercy of God, the Life-Creating Pillar.
The Robe of the Lord, actually one of its four parts, the lower portion specifically (other parts of the Robe of the Lord are also known in Western Europe: in the city of Trier in Germany, and in Argenteuil near Paris in France), just like the Chiton of the Lord, came to be in Georgia. In contrast to the Chiton, the Robe portion was not kept underground, but was in the treasury of the Svetitskhoveli cathedral right up to the seventeenth century. Then the Persian Shah Abbas I, in devastating Georgia, along with other treasures also carried off the Robe of the Lord. In order to ingratiate himself with Tsar Michael Feodorovich, the Shah sent the Robe of the Lord as a gift to Patriarch Philaret (1619-1633) and Tsar Michael in 1625. The authenticity of the Robe was attested by Nectarius, Archbishop of Vologda, also by Patriarch Theophanes of Jerusalem, who had come from Byzantium, and by Joannicius the Greek, but especially also by the miraculous signs worked by the Lord through the venerable relic.
Afterwards two parts of the Robe came to be in Peterburg: one in the cathedral at the Winter Palace, and the other in Sts Peter and Paul cathedral. A portion of the Robe was also preserved at the Dormition cathedral in Moscow, and small portions at Kiev’s Sophia cathedral, at the Ipatiev monastery near Kostroma and at certain other old temples. At Moscow annually on July 10 the Robe of the Lord is solemnly brought out of a chapel named for the holy Apostles Peter and Paul at the Dormition cathedral, and it is placed on a stand for veneration during the time of divine services. After Liturgy they carry the Robe to its former place.
On this day a service to the Life-Creating Cross of the Lord is proper, since the Placing of the Robe in the Dormition cathedral in 1625 took place on March 29, which happened to be the Sunday of the Veneration of the Cross during the Great Fast.
From the Prolog:
At the time of the suffering of our Lord Jesus for mankind, there was to be found among the ranks of the Roman army in Jerusalem a Georgian named Elioz from the town of Mtskheta. His mother had heard of Christ and, in her heart, believed in Him. Seeing her son off to the army in Palestine, she counseled him not to do anything against Christ. When the Lord was nailed to the Cross, the sound of the hammer on Golgotha reached the ears of Elioz’s mother in the town of Mtskheta. Hearing this sound, she cried out: “Woe is me because I did not die before this time. Death would have rescued me from this dreadful sound!” Saying this, she fell dead. Elioz, at that time, was beneath the Cross and with the other soldiers cast lots for the tunic [robe] of Christ. He won the vesture and brought it to Mtskheta and gave it as a gift to his sister Sidonia. She, having heard about the death of the Lord and that her brother was a participant of the shedding of innocent blood, fell dead holding the tunic of the Lord firmly in her hands and no one was able to tear it away but were compelled to bury the tunic with her. A cedar tree sprouted from her grave from which poured forth a sweet-smelling healing myrrh. In time, the cedar tree fell and the place was forgotten. Following her prayer, St. Nina, found this place with the help of a pillar of fire. The baptized Emperor Mirian erected a church there dedicating it to the Holy Apostles. In the year 1625 A.D., the Shah Abbas took this tunic and sent it to Moscow as a gift to Prince Michael Feodorovitch and Patriarch Philaret. This tunic was placed in the Cathedral Church of the Dormition [Assumption] of the Blessed Virgin in Moscow.