Noir Drive

In Sydney in 1952 and returning from a month away, the private investigator Reilly finds his office has been taken over by the building's janitor, Jerry Vane, who has been impersonating him in his absence. Roughing Vane over, Reilly discovers he has taken a missing person's case in which an insurance company is trying to locate someone named Alex Pleshette. However, when Reilly presents himself to the insurance office to drop the case, the owner Max Arnett claims he never hired his agency to begin with. On the way out however, Arnett's receptionist inadvertently gives away the truth that Reilly was in fact hired.
Heading back to his office, Reilly is confronted by two thugs in an alley who beat him and tell him to lay off the Pleshette case. In his office a short time later, a beautiful young woman in black arrives. Presenting herself as Mrs. Pleshette, Reilly assumes she is Alex Pleshette's wife, however she curtly informs him that her husband is dead, and that she is actually Alexandra, better known as Alex Pleshette. She tells him to stop interfering as she is now no longer missing, and departs â leaving him even more confused.
Next day, Reilly finds out from his police detective friend Jack Bosley that Alex Pleshette witnessed the murder of her husband, a wealthy tycoon named Donald Pleshette who was at the time being investigated for company insurance fraud. However, she was knocked unconscious by the killer and as a result is unable to remember the event. Not long after this, she went missing and no one knew where she was, not even her lover Gabe Preston, her husband's disgruntled business partner. Reilly recognizes that Preston would thus have a motive for murder, but Bosley explains that he has a strong alibi.
Later, Reilly gives Vane a camera and instructs him to follow Arnett and take photos of anything that appears interesting. Meanwhile, he drives to the Pleshette mansion on Noir Drive to confront Alex. She concedes that although she was bitter towards her husband as a result of the fraud allegations against him, she had no proof that her husband was even involved in the fraud, and that even if she did she couldn't disclose them because of the legal principle of marital privilege, whereby spouses cannot testify against each other. They are then interrupted by the arrival of Gabe Preston. Alex introduces them before promptly leading Reilly out of the house. On his way out, Reilly explains to Alex that whoever hired him did so on the instruction of her husband's killer, worried that she may regain her memory at any time, and wanting her close by if she did. Reilly says he believes she knows more than she realises, but she replies "at times we all want to be kept in the dark".
Back at his office, Reilly looks through the photos taken by Vane, and in one sees Max Arnett meeting up with Gabe Preston. He promptly calls Bosley, who confirms that Preston's alibi was in fact Arnett. Reilly rushes off to the Pleshette mansion but Preston and Alex have left for good.
Far way on a tropical island resort, Preston and Alex lounge back on a beach. Alex however is unsettled â her memory then triggered by the pop of the champagne cork â and she realises it was Gabe Preston who murdered her husband. Looking down to reveal the wedding ring she now wears as Mrs. Alex Preston, it occurs to her that Preston now not only has access to the entire fortune, but that she is unable to testify against him because of marital privilege.

Question: What does Reilly give Vane?
Answer: a camera; a camera