Spoiler: Teije's Former Flame?

So I didn't read the book but I was wondering if Teije's former girlfriend was the hacked up corpse they found in the water? Anyone know from the book? When Lucy initially broke into the locked file cabinet her facial expressions were became alarming as she viewed the former girlfriend's facial expressions becoming more concerningly subdued, most likely due to Teije's increasing obsessiveness. All three of Teije's female interests followed that same pattern in his photographs??? And Teije did say she disappeared and he never heard from her again. Some of the sound was difficult for me to understand so I might have missed something. I certainly could not understand what Lucy said about her friend's father and cider??? If the cops thought Teije might have killed Lily why didn't they search his home?