Blanka Zmigrod was 68 years old when she was shot in the head on the way home from work in 1992.
John Ausonius, now aged 63, is serving a life sentence for carrying out a series of shootings against eleven people between August 1991 and January 1992, in racially motivated attacks on migrants.
Police found that he had been in Germany in February 1992 and encountered Ms Zmigrod at a restaurant where she worked as a coat-check attendant in Frankfurt a week before she was killed. It's alleged that he accused her of stealing an electronic pocket calendar.
Detectives from Germany interviewed Ausonius at Kumla Prison in 1996, but he was never charged. He denies having any involvement in Ms Zmigrod's death and his lawyer has doubts whether he can be extradited after so much time.
"To defer investigating a suspicion until after so many years have passed, and we are talking of about 20 years, is of course totally unacceptable," Thomas Olsson told tabloid Aftonbladet.
Two years ago, German police returned to question the man named "Laser man" by the Swedish media after he used a rifle fitted with a laser sight to kill one of his victims.
Now a European arrest warrant has been issued.
"Germany requests that John Ausonius be handed over for trial of the suspected murder in Frankfurt in 1992," says chief prosecutor Krister Petersson at the International Public Prosecution Office in Stockholm to news agency TT.
Lawyer Thomas Olsson tells TT that they will oppose the extradition order.
"We have not seen the German request yet, but the starting point is of course that he opposes a transfer."
Ausonius, who had a Swiss father and a German mother who had emigrated to Sweden, told Aftonbladet that he doubted the extradition order had legal susbstance.
"I question whether they really have the right to bring a prosecution after all these years."