Talk with the neighbors. Set up video from a neighbors house if you can.
Keep the detectives number and when he is caught, as these guys are like sharks, they keep coming back.
I suggest a Taurus Judge or Magnum handgin loaded with .410 shotgun shells. Eventually they graduate to worse crimes. What if he brings a friend next time, in the middle of the night.
I dont keep large dogs, but I do keep two small chihuahuas. You cant beat their nose or ears, or eyes.
If you havent recorded the serial numbers on everything in your house, do so. To include photos for anything over $25 dollars.
If you know where he is jumping the fence, he is probably hanging out there and has your routine. Get some used cat litter, and place where he has to satnd. Cat poop smell does not go away easily.
I like plants the have stickers for under windows. 4 foot rose bushes dont play.
I would take some 80 pound test fishing line, double it, and put it where you wont get into it, but the crook will close line himself.
I can go on all day.