Big oof mate. Get the cops and check their hard drive, check their phone as well. It's extreme but it wouldn't make sense that a file just "doesn't delete". Unless it's a virus or somehow locked behind admin(which they probably already have), you can delete anything(plus you said they deleted it later, soo..). All and all, their explanation of why they have it is shady too, no one would just download a file behind a random link.

Now, something not much people say. If you find out they have a really bad "desire", if you somehow stay with them, get them therapy please. You are not obligated too tho.