It does him no good anyway since once the insurance company pays you, they will almost certainly come after him directly-- by paying you they are subrogated to your claim against him.
I would imagine the terms of your lease state what is to happen in the event he causes damage, and unless the lease says that you are compelled to do what he is asking for, you should be well within your rights to refuse his request.
You are under no obligation to submit an insurance claim.
The information presented here is general in nature and is not intended, nor should be construed, as legal advice. This posting does not create any attorney-client relationship with the author (who is only admitted to practice law in the State of California). For specific advice about your particular situation, consult your own attorney.