Mr. Conrad was an imaginary accomplice of serial killer Adam Rain, who appeared in The Lesson.
Background
Not much is known about Mr. Conrad, as he is a puppet with no real background. What is known is that when Adam recovered from a coma induced by a serious car accident, Mr. Conrad became his only friend and convinced him to start his series of killings.
The Lesson
Throughout the episode, Mr. Conrad is assumed to be an actual person aiding Adam. However, a few giveaways are provided throughout the episode: his oddly, extremely short stature; the fact that Adam is the only one who talks to him and vice-versa; and the victims only pay attention to Adam when both him and Mr. Conrad are in the room. He participates in Adam's play The Robbery, in which he portrays the robber who killed Adam's father Alex. However, the BAU interrupt the play and reveal that Mr. Conrad was a puppet the entire time.