Upon realizing the victim's dying message on the glass cup is very similar to the missing letters on the mirror in Kohji Haneda's room, Conan and Subaru each rearrange the missing letters and discover Haneda's dying message:
Since the dying message was "P T O N", the answer to it must contain all of the missing letters of "U MASCARA"
PUT ON MASCARA - P T ON = U MASCARA
U MASCARA - ASACA (for "Asaka" in English) = U M R
Which can be rearranged to make RUM
making the answer "ASACA RUM"
Masumi calls Mary "Mama", indicating that she is her mother.
The only information that the victim had was that he believed Asaka to be a woman. He was going to pretend that he had summoned Kohji's spirit and have it say that a woman was going to kill him. The culprit said that someone saw Asaka holding "that small mirror".
Conan considers that if Asaka is Rum, then perhaps what Haibara said about being feminine refers to looking girly on the outside but strong like a man on the inside. If Rum had been a bodyguard 17 years ago, then they must be old now. Conan also ponders the possibility that Mary is Rum after having shrunken, being girly yet strong and older than she looks.