Sadly, this is one of the most common occurences in domestic-violence situations: To control their victim, an abuser targets other living beings that have the least ability to defend themselves or speak out about the abuse and to which the victim often has the greatest emotional attachment--typically any children in the household and, to an even greater extent as far as vulnerability, family pets.
While unfortunately you cannot bring your cat back to life, your ex-boyfriend can and should be prosecuted criminally and civilly for intentionally causing you emotional distress and destroying your property without your knowledge or permission. Have you called the police? If not, do so immediately and make a full report.
Also, lodge a complaint against the humane society for its actions. I wholeheartedly agree with the attorney who said that the shelter should be held contributorily liable because they should not have just said, "OK, we'll put the animal down" without first checking for some kind of documentation of ownership.
Indicia of ownership can include such things as vet records, government licensing and rabies vaccination records, pet food and pet product receipts, purchase/adoption records, third-party observations of who provided more "care, custody and control" - e.g., Who did the animal spend more time with/reside with the longest? Who remembered when vaccinations came due? Who renewed the city dog license? Leave no stone unturned because the person with the most evidence of caretaking usually wins in these situations.
Best of luck to you!
Joan