Josephus Antiquities of the Jews Book 8.4.1
And when this invitation of the whole body of the people to come to Jerusalem was every where carried abroad, it was the seventh month before they came together: which month is by our countrymen called Thisri; but by the Macedonians Hyperberetæus. The feast of tabernacles happened to fall at the same time: which was celebrated by the Hebrews as a most holy and most eminent feast. So they carried the ark, and the tabernacle which Moses had pitched, and all the vessels that were for ministration to the sacrifices of God, and removed them to the temple. The King himself, and all the people, and the Levites went before, rendring the ground moist with sacrifices, and drink-offerings, and the blood of a great number of oblations; and burning an immense quantity of incense;
Sotah 9aBabylonian Talmud
With regard to David, the citadel that housed his home and city, was not destroyed, as it is written: “Her gates are sunk into the ground” (Lamentations 2:9), as the gates of Jerusalem built by David were not destroyed by enemies, but sunk into the ground and were buried there. This is also so with regard to Moses, as the Master said: When the first Temple was built, the Tent of Meeting was sequestered, including its boards, its clasps, and its bars, and its pillars, and its sockets. The Gemara asks: Where is it sequestered? Rav Ḥisda says that Avimi says: Beneath the tunnels of the Sanctuary.
Notes and References
"... More evidence that the Tabernacle was actually in the first temple came from the Bible itself. If we look at the report of the events of the day that King Solomon dedicated the Temple, which appears in both the books of 1 Kings and 2 Chronicles, it says: And they brought up the ark of Yahweh and the Tent of Meeting and all of the holy implements that were in the Tent. It says explicitly that the Tabernacle was brought up to the Temple along with the ark and the implements. The Tabernacle may then have been set up under the cherubs' wings, or it may have been stored away in the Temple precincts while the correspondingly measured space under the wings stood for it. Either way, the Tabernacle was linked to the first Temple. Josephus, the Jewish historian of the first century A. D., also says explicitly that the Tabernacle was brought into the Temple. And he states that the effect of the cherubs' having their wings spread was precisely to appear as a tent. Also, the Babylonian Talmud, compiled in the fifth century A. D., says that the Tent of Meeting was stored away beneath the Temple ..."
Friedman, Richard Elliott Who Wrote the Bible? (p. 183) Harper San Francisco, 1997