Insurance on a motor vehicle, whether a personal policy or business policy covering a company work truck, does not cover the cost of a moving violation citation or traffic ticket.

Auto insurance covers the driver in case of an accident. For example if the company's insurance on the truck is basic liability insurance then that normally would include property damage and bodily injury coverages.

Property damage liability insurance covers you if your car damages someone else's property. Usually it is their car, but it could be a fence, a house or any other property damaged in an accident.

Bodily injury covers other people's bodily injuries or death for which you are responsible.

If the work truck also has physical damage coverages then this would include collision and comprehensive that cover the vehicle. Collision insurance covers damage to your car when your car hits, or is hit by, another vehicle, or other object.

Comprehensive covers your vehicle, and sometimes other vehicles you may be driving for losses resulting from incidents other than collision. For example, comprehensive insurance covers damage to your car if it is stolen; or damaged by flood, fire, or animals.

Your boyfriend may discuss if the company he works for will help him out with taking care of the traffic ticket but likely he will need to personally take care of the ticket by calling the court listed on the ticket and paying a fine.