A. A claimant dissatisfied with the rejection of his demand, or with the amount allowed thereon, may sue the county therefor at any time within six months after final action of the board, but not afterward. If in the action judgment is recovered for more than the board allowed, the board shall allow and pay the judgment, together with the costs adjudged, but if no more is recovered than was originally allowed by the board, the board shall pay the claimant only such amount.
B. A claimant may accept the amount allowed and sue for the balance of his demand, and this action shall not be barred by the acceptance of the amount allowed.