The claim of an employee, including, but not limited to, any peace officer or firefighter, for compensation does not affect his or her claim or right of action for all damages proximately resulting from the injury or death against any person other than the employer. Any employer who pays, or becomes obligated to pay compensation, or who pays, or becomes obligated to pay salary in lieu of compensation, or who pays or becomes obligated to pay an amount to the Department of Industrial Relations pursuant to Section 4706.5, may likewise make a claim or bring an action against the third person. In the latter event the employer may recover in the same suit, in addition to the total amount of compensation, damages for which he or she was liable including all salary, wage, pension, or other emolument paid to the employee or to his or her dependents. The respective rights against the third person of the heirs of an employee claiming under Section 377.60 of the Code of Civil Procedure, and an employer claiming pursuant to this section, shall be determined by the court.