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>> Therefore the "Keys" were not given to the disciples in general; they were given to the person Jesus was speaking to, Peter, in virtue of the office he had just received from Jesus.<<

Then please show documentation that Peter passed them on to anyone.

By "passed them on," I suppose you mean, "Passed on the authority of his ministry" (since we are not talking about physical keys). After Peter's martyrdom in Rome, his successor was Linus. Here's the requested documentation:

Irenaeus: "The blessed apostles, then, having founded and built up the Church, committed into the hands of Linus the office of the episcopate." Against Heresies 3:3.3

The Oxford Dictionary of Popes interprets Irenaeus as classifying Linus as the first bishop of Rome. J. N. D. Kelly, Oxford Dictionary of Popes, 2005

Linus is presented by Jerome as "the first after Peter to be in charge of the Roman Church""Post Petrum primus Ecclesiam Romanam tenuit Linus" -Chronicon; 14g (p. 267)

Eusebius calls Linus "the first to receive the episcopate of the church at Rome, after the martyrdom of Paul and Peter" Church History 3.2

John Chrysostom wrote, "This Linus, some say, was second Bishop of the Church of Rome after Peter",Homily 10 on 2 Timothy

The Liberian CatalogueThe Chronography of 354 AD. Part 13: Bishops of Rome presents Peter as the first Bishop of Rome and Linus as his successor in the same office.