1. (b) That's right. An agent who has authority to create contractual obligations for a principal may or may not have the authority to represent the principal in the discharge of those obligations. This may be important in relation to the question of making or receiving payments due under a contract between a principal and third party. If the agent has the necessary authority, then payment made by the third party to the agent is valid as a payment to the principal. But, in the absence of the necessary authority, any payment to the agent does not discharge the third party's obligation to the principal.

In the present case, B clearly has no express or implied authority to receive payment on behalf of A. It follows that by paying B, the customer has not discharged her obligations to A.