that I don't know. The inventio of the relics in Jerusalem dates to 415 and they began to circulate soon after that. Augustine discusses it in City of God. From what I've been able to tell San Lorenzo is the main place they were deposited but I don't know when.

That well-known movement of relics to the west and Constantinople makes the silence about Rome perplexing. A church on the Via Latina was built a little before the Rotondo; Stephen is in Pelagius II's S Lorenzo mosaic; and a 7th cent. text says a monastery by S Paolo flm held one of the stones (!).