B) Correct. Monitoring serum theophylline levels is crucial when caring for a client receiving theophylline therapy. Theophylline has a narrow therapeutic range, and monitoring blood levels helps ensure therapeutic effectiveness while minimizing the risk of toxicity. The nurse should assess the client's theophylline levels regularly and adjust the dosage as necessary.

A) Incorrect. While blood pressure monitoring is important, it is not the priority assessment specifically related to theophylline therapy.

C) Incorrect. Theophylline can affect liver function, but liver function tests are not the priority assessment in this case.

D) Incorrect. Pulmonary function tests are not directly related to theophylline therapy and do not require prioritization in this scenario.