How can Itachi use his Mangekyō Sharingan after death?
As it comes straight from the Naruto wikia:

Edo Tensei




  The Summoning: Impure World Reincarnation binds the soul of a deceased
  person to a living vessel, restoring them as they were when they were
  alive in order to do their summoner's bidding.


So that's why Itachi had both of his eyes, because he was restored in the state before he died, which he had both of his eyes.