The victim, identified only as Maria D., was 43-years-old and had lived in Germany for “a few years” but without a permanent home.
The authorities say the murder is a crime of extreme violence as Maria D. had been dismembered.
The river Elster, which flows through Leipzig, was the scene of intense forensic activity after the discovery of her torso under a bridge by a passer-by last Thursday.
Days later the police divers managed to locate the missing limbs.
Maria D. was last seen on April 9th by her former partner, Toni, also Portuguese. The pair emigrated to Germany five years ago but separated recently.
Toni, 43, described Maria D. as a "cheerful and sociable person", and had no explanation at all for her murder.
The German authorities have no doubt that this was a viloent murder and now are looking for witnesses who may have been with Maria D. during the last weeks of her life.
Maria's disappearance was not reported to the authorities and according to the newspaper Leipziger Volkszeitung, it is not clear if she had been staying with friends or in a hostel for homeless people.
