Final answer:
A nurse should refer a stroke patient for occupational therapy when there is a loss of strength and movement in one arm, aiding in recovery and daily living skill adaptation.
Step-by-step explanation:
The nurse on a med-surg unit assessing a client who has had a stroke should initiate a referral for occupational therapy when observing a client with loss of strength and movement in one arm. Occupational therapy can significantly aid in the recovery and rehabilitation process by helping patients relearn daily living skills and adapt to any residual physical limitations. The other symptoms mentioned, such as difficulty speaking and memory issues, may require speech therapy or neurology specialists, respectively.