John Ausonius, 64, has already received a life prison term in Sweden for a six-month shooting spree in 1991-92 in which he killed an Iranian student and wounded 10 other immigrants.
The convict was extradited to Germany in late 2016 to face trial for one additional murder -- of 68-year-old Jewish Holocaust survivor Blanka Zmigrod in Frankfurt in 1992.
The verdict for Ausonius, who denies the woman's murder, was to be announced around 1330 GMT by justice Baerbel Stock in the Frankfurt court.
Born as Wolfgang Alexander Zaugg in Sweden to a German mother and a Swiss father, Ausonius was reportedly bullied at school, rejected his foreign origins and later developed a strong hatred for immigrants.
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He would dye his dark hair a lighter shade and wear blue contact lenses to appear like a "real Swede", Frankfurter Allgemeine Zeitung has reported.
He obtained Swedish citizenship as a young adult and changed his name twice, finally to Ausonius after a Roman poet.
Norwegian mass murderer Anders Behring Breivik, speaking at his Oslo trial for the 2011 killings of 77 people, mentioned the "Lasermannen" or "laser man" as a figure who shared the same goals.
Displaying a pattern of antisocial behaviour and violent outbursts, he went on to commit a string of bank robberies.
His spate of racist gun attacks started when he fired at a 27-year-old Eritrean student in August 1991, wounding him.
Ausonius later killed the 34-year-old Iranian Jimmy Ranjbar with a shot to the head and badly wounded another nine victims, from countries including Brazil, Greece, Syria and Zimbabwe, in his shooting spree, which went on until January 1992.
Zmigrod, the Frankfurt victim, was born in Poland, survived several Nazi concentration camps including Auschwitz, and later lived in Israel before moving to Germany in 1960, according to a Swedish documentary.
Investigators have not, however, established whether the crime was motivated by anti-Semitism.
German prosecutors say Ausonius was seen arguing with the woman, a hotel restaurant wardrobe attendant, 36 hours before her death, accusing her of having stolen his Casio electronic device.
They charge that he killed her near her home with a close-range shot to the head and took her handbag in the apparent belief it contained the device on which he had stored the numbers of his foreign bank accounts.
If the German court does not find him guilty, he will be taken back to his jail cell in Sweden.