The Killer is Werner Fossmo.

Werner and Jenny Moore had an affair. Jenny wanted moore (clue: her latest CD).

Werner had, at a weak moment, given Jenny a necklace that had been in his family for generations (clue: photos of Jenny and the photos hanging on the wall at Werner’s house)

Jenny wore the necklace the night she was killed. Werner took his wife to a restaurant that evening, he then drugged her (clue: she got tired).

Later that night Werner drove over to Jenny’s house and killed her. He took the necklace. His wife found it the day after and thought it was a present for her (clue: the last picture of the wife)