The mystery of Sauron's lost finger

[Tuor of Gondolin]

Elrond approached Aragorn and presented him with the heirlooms of his line. One was the Scepter of Arnor-- and the other, a mysterious gift carefully wrapped in black cloth.

“You, Aragorn son of Arathorn, are the rightful King of Gondor. Take these heirlooms which have been bestowed upon thee in honour and rule well! Here is the Scepter of Arnor,” and he carefully placed it in Aragorn’s hands, “and…the One Finger.” Elrond raised the small item and unwrapped it as one would with a deadly creature. And behold! in the midst of the cloth there lay a black finger. It seemed no less fearful than if it was still attached to its master’s hand and emitted a cold chill into the air.

Aragorn looked upon Elrond with disbelief and fear. “The Finger? The one that was severed from Sauron’s hand? Alas! that is a foul token!”

So according to the above Elrond gave Strider the finger!
Perhaps PJ's crabby patty Elrond was correct after all.