The same way Sybil salvaged her Time-stream viewing doodad. By going directly to the source and salvaging it from Coulson's ruined robo-corpse after the explosion. In control of the lighthouse, Deke would have had direct access to the blast sight.
Coulson destroyed the Chronicom's ship. And with it, presumably their ability to move through time. Sybil is stuck in the 80's same as Deke and Mack, prior to the Zephyr's return. Or at the very least, because she had lost her Time Stream reader, and could no longer safely predict what any changes she might make would do to the timeline moving forward. Now she has her Time Reader so she can predict the future and make changes again. But she appears to still be stuck going to the long way round.