Cortana. Campaign quesition.

How did chief get Cortana back without having her chip in the 5th mission. Chief uploads Cortana and the the Librarian abducts her. While Chief is looking for her he doesn’t pick up the chip and when he speaks to the Librarian Cortana shows up in another podium and somehow gets transferred back to chief without the chip.

Take a look

at 44:40 and 50:45

It’s magic. Never heard of it?

Video game logic

An easy explanation is that while Chief was interacting with the Librarian- she had the data platform delivered into the room so he could retrieve Cortana from it.