When a Catholic family member or friend has died, please contact a funeral agency as soon as possible. You can search for authorised funeral agencies in Sweden here. Tell the funeral agency you have chosen that you wish a Catholic funeral service for the deceased person.
If the deceased person was a member of a Catholic parish you should then contact the priest you want to hold the funeral service. If you don't have any specific priest in mind you can just contact the parish and they will help you further with the arrangements. If you don't know which parish the deceased person belonged to you can search here by using a postal code.