An item was stolen that has a replacement cost of about~ 600 dollars. (I had lent it to my mother and my brother had it in his car for transport when it was broken into). We have a deductible of 500 dollars that may apply. If we file a claim for this stolen item, will our home owners insurance go up? There was a police report filed for the break in and theft and the receipt for the item was saved.

if it cost you $600 and you have a $500 deductible at most you will save $100 your insurance cost WILL increase, it's not worth it.

Yes, it does. If your claim is paid, it's worth AT MOST $100.

Because you get depreicated value up front, and replacement value after you replace it, you might as well replace it first, and turn in the receipt at the time you file the claim - BOTH receipts.