INSURER'S RIGHT OF RECOVERY.

(a) An insurer that makes a payment to any person under any coverage required by this subchapter is subject to the terms of that coverage and, to the extent of the payment, is entitled to the proceeds of any settlement or judgment resulting from the exercise of any right of recovery of the person to whom the payment is made against any person or organization legally responsible for the bodily injury, sickness, disease, or death for which the payment is made, including the proceeds recoverable from the assets of an insolvent insurer.

(b) If, under an insurance policy issued under this subchapter, an insurer makes a payment as a result of the insolvency of another insurer:

(1) the insolvent insurer's insured shall be given credit to the extent of the paying insurer's payment in any judgment obtained against the insured with respect to the insured's legal liability for damages described by Subsection (a); and

(2) subject to Subchapter F, Chapter 462, the paying insurer has the right to proceed directly against the insolvent insurer or that insurer's receiver, and in pursuing that right the paying insurer has any rights that the insolvent insurer's insured might otherwise have had if the insured had made the payment.