My Punto was hit from behind by Honda City – How to claim insurance

HI,

My punto met with an accident, a honda city car hit my punto from behind – I have to replace bumper, fog lights. Malik Cars, Hyderabad gave a quote of 7k for the repair.
Bumper: 2500/-
Rear fog lamps: 800/-
Paint: 3300/-
Service Charges: 200/-
total: 6950/-
Out of this: ~3k needs to be paid by me.
The honda city owner told me that he would pay the expenses that are not covered by insurance company. I have his contact number and the honda city car number. I have not registered any FIR etc.

Can you pls tell me how to proceed with this claim?
If I claim from my insurance policy i would loose no claim bonus. Whats the procedure to claim third_party damages from the honda city’s insurance policy?

Thx,