Final answer:
The correct GCS documentation for a client who shows no eye opening, verbal, or motor response is a score of 3, indicating a state of deep unconsciousness or coma.
Step-by-step explanation:
The Glasgow Coma Scale (GCS) is a clinical tool used to assess and calculate a patient's level of consciousness after a brain injury such as a stroke. According to the scenario where the client does not open eyes, does not respond to painful stimuli, and makes no sounds, the correct documentation in the electronic medical record reflecting the GCS score should be: 'Score of 3 on the GCS.' This score represents the lowest possible score on the GCS, indicating deep unconsciousness or coma.