(a) That's right. When faced with an anticipatory breach of contract, the aggrieved party has a choice. The choice is between continuing with performance of the contract, reserving a right to claim damages for any losses flowing from the breach, or to stop (terminate) performance of the contract, and claim damages for losses. In this case, A has clearly elected to affirm the contract, not to terminate performance.
The effect of this choice is to 'wipe out' an anticipatory breach, so that thereafter it is no longer open to A to terminate performance unless there is a fresh repudiation or breach.