Final answer:
Dr. Roylott needed Helen to move to her sister's former room to facilitate his plot using a snake to prevent her from marrying and thus keeping control of the inherited wealth.
Step-by-step explanation:
In "The Adventure of the Speckled Band," Dr. Roylott needs Helen to move to her sister's former room as part of a sinister plot. Dr. Roylott's plan involves a deadly snake, and the ventilator and bell-pull in the sister's room were central to facilitating this perilous scheme. The room Helen was asked to move into had a ventilator that connected to Dr. Roylott's room, through which he could send the snake to carry out his nefarious act without direct involvement. Moreover, the fake bell-pull served as a route for the snake to travel back and forth. Dr. Roylott's motive behind this was to maintain control of the inherited wealth, which would be compromised if Helen were to get married.