Sweeney Todd: The Demon Barber of Fleet Street

In 1846, Benjamin Barker, a barber, arrives in London, accompanied by sailor Anthony Hope. Fifteen years earlier, he was falsely convicted and sentenced to penal transportation by the corrupt Judge Turpin, who lusted after Barker's wife Lucy. Barker adopts the alias "Sweeney Todd" and returns to his old Fleet Street shop, situated above Mrs. Nellie Lovett's meat pie shop. He learns that Turpin raped Lucy, who then poisoned herself with arsenic. The couple's daughter, Johanna, is now Turpin's ward, and is the object of Turpin's lust. Todd vows revenge, and re-opens his barber shop after Mrs. Lovett returns his straight razors to him. Anthony becomes enamored with Johanna, but is caught by Turpin and driven away by his corrupt associate, Beadle Bamford.
Todd denounces faux-Italian barber Adolfo Pirelli's hair tonic as a fraudulent mix and humiliates him in a public shaving contest. A few days later, Pirelli arrives at Todd's shop, with his boy assistant Tobias Ragg. Mrs. Lovett keeps Toby occupied while Pirelli identifies himself as Todd's former assistant, Davy Collins, and threatens to reveal Todd's secret unless Todd gives him half his earnings. Todd kills Collins to protect his secret, and hides his body in a trunk.
After receiving advice from Bamford, Turpin, intending marriage to Johanna, visits Todd's shop for grooming. Todd shaves Turpin, preparing to slit his throat; they are interrupted by Anthony, who reveals his plan to elope with Johanna before noticing Turpin. Turpin leaves enraged and Todd vents his rage by killing customers while waiting for another chance to kill Turpin, and Mrs. Lovett bakes the victims into pies. Todd rigs his barber's chair with a pedal-operated mechanism that deposits his victims through a trapdoor into Mrs. Lovett's basement bakehouse. Anthony searches for Johanna, whom Turpin has sent to an insane asylum upon discovering her plans to elope with Anthony.
The barbering and pie-making businesses prosper, and Mrs. Lovett takes Toby as her assistant. Mrs. Lovett tells an uninterested Todd of her plans to marry him and move to the seaside. Anthony discovers Johanna's whereabouts and, following Todd's suggestion, poses as a wigmaker's apprentice to rescue her. Todd has Toby deliver a letter to Turpin, telling him where Johanna will be brought when Anthony frees her. Toby has become wary of Todd and tells Mrs. Lovett of his suspicion.
Bamford arrives at the pie shop, informing Mrs. Lovett that neighbors have been complaining of the stink from her chimney. He is distracted by Todd's offer of a free grooming and is murdered by Todd. Mrs. Lovett informs Todd of Toby's suspicions, and the pair search for Toby, whom Mrs. Lovett has locked in the bakehouse. He has hidden himself in the sewers after seeing Bamford's body drop into the room from the trapdoor above, as well as finding a human toe in a pie. Meanwhile, Anthony brings Johanna, disguised as a young sailor, to the shop, and has her wait there while he leaves to find a coach.
A beggar woman enters the shop in search of Bamford, and Johanna hides in the trunk. She recognizes Todd, but upon hearing Turpin coming, Todd quickly kills her and sends her through the trapdoor. As Turpin enters, Todd explains that Johanna had repented and is coming to him, then offers a free shave in the meantime; as Turpin finally recognizes Todd as Benjamin Barker, Todd stabs him several times before cutting his throat and sending to the bakehouse as well. Johanna comes out of her hiding place still disguised as a boy, and Todd prepares to slit her throat as well, not recognizing her as his daughter. However, hearing Mrs. Lovett scream in horror in the basement as a dying Turpin grabs her dress, Todd lets Johanna go.
Todd discovers that the beggar woman was his wife Lucy, whom he believed to be dead, and that Mrs. Lovett misled him about her death. Todd pretends to forgive her and dances with her before hurling her into the bakehouse oven, then cradles his wife's dead body in his arms. Toby climbs from the sewers and Todd allows Toby to slit his throat with his own razor. Toby leaves the basement as Todd bleeds to death over his dead wife.

Question: Who does Todd discover the beggar woman really is?
Answer: his wife Lucy