. . . Jesus took His Shroud with Him out of the empty tomb
and later gave it to the Apostle John, seems the most likely [possibility].
He writes today in part 1 of what will be multiple installments of an article on the servant of the priest:
Introduction. The Gospels don’t record that Jesus’ burial shroud [sindon] was in the empty tomb. Indeed, despite the desire by most Shroud pro-authenticist to place the Shroud in the empty tomb, included among the othonia, or even as the soudarion, both mentioned in (Jn 20:5-7), the evidence is that it wasn’t there. What Peter and John saw in the empty tomb, as recorded in Luke 24:12 and John 20:5-7, was the linen strips [othonia] which had bound [edesan] Jesus’ hands and feet and the spices (Jn 19:40), as well as the sweat-cloth [soudarion] (the Sudarium of Oviedo) which had been on [epi] Jesus head, but no Shroud [sindon]. From seeing this arrangement of the othonia andsoudarion but no sindon, John believed that Jesus had risen from the dead (Jn 20:6-9). Several early Christian writings record that the resurrected Jesus took His shroud with him out of the tomb and gave it to different individuals. The earliest and most highly regarded of these writings, the late first/early second century The Gospel of the Hebrews records that after His resurrection Jesus gave his shroud [sindon] to "the servant of the priest." Since it seems incredible . . . .
FYI: The following quotation is taken from Wikipedia which sources it from the critical 3rd German edition of Schneemelcher’s New Testament Apocrypha, translated by George Ogg:
And when the Lord had given the linen cloth to the servant of the priest, he went to James and appeared to him. For James had sworn that he would not eat bread from that hour in which he had drunk the cup of the Lord until he should see him risen from among them that sleep. And shortly thereafter the Lord said: Bring a table and bread! And immediately it is added: He took the bread, blessed it and brake it and gave it to James the Just and said to him: My brother, eat thy bread, for the Son of man is risen from among them that sleep.