Final answer:
The nurse manager is showing shared leadership by involving the staff nurses in the survey development and administration process for a client-first initiative.
Step-by-step explanation:
When the nurse manager asks the staff nurses to develop and administer a survey to patients before discharge, as part of the 'customer (client) first' initiative, he/she is demonstrating shared leadership. This approach involves engaging the nurses in decision-making processes and making them active participants in the initiative, thereby distributing leadership responsibilities and promoting team effectiveness.