No, as long as you have let your insurance company know they car is stolen.
I think that your insurance covers the items that were yours that were stolen, and the company's covers the car damage.
Tell the police, tell the insurance company
If you only carry liability insurance, that is all that the insurance company is liable for in this state.
That is up to the discression of the insurance company.
"Most engagement rings represent a substantial value and would be devastating to lose, both financially and emotionally. Insurance helps protect the financial value if the rings would be lost or stolen."
I recommend you contact your insurance company, and inform them of the recovered goods
Once the insurance company has paid the claim for stolen items they become the legal owners of the items.
i'd say the insurance company owns it
It belongs to the insurance company
If you have not settled with the insurance company you will have to take it back. If the insurance has paid out it is their car.
You should report the theft immediately to the police and to the car owner's insurance company.