Is it permissible to exaggerate or deliberately amplify the description of damages from a car accident in order to avoid future financial losses, knowing that the other party is at fault?

There is no harm in taking what you are entitled to for the actual damage incurred by your car from the insurance company. However, fraud, claiming non-existent damages, or exaggerating them to deceive the insurance company, is impermissible. This is taking money unjustly, and deception and fraud are forbidden. The Prophet, peace and blessings be upon him, said: "Whoever cheats is not one of us," and "Whoever cheats us is not one of us. Deceit and fraud are in the Hellfire."