La Donna Che Visse Due Volte by Boileau-Narcejac

A retired detective with a crippling fear of heights is hired to shadow a client's enigmatic wife, who seems possessed by the past; he becomes obsessed and falls in love, and when she dies after a fall his guilt and longing drive him to pursue a younger woman who resembles her. As he attempts to recreate and possess the lost ideal, deception and manipulation are revealed and the boundary between reality and illusion collapses into a tragic psychological unraveling.

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