How long should aphasia last after a first stroke?

Hard to say. It depends on the size, location, and severity of the stroke to tell how long the aphasia will last. I know this is vague, but your local neurologist should be able to tell you this answer as he evaluates your loved one with stroke.
It varies. It is recommended to have a speech/langauage therapist to work with stroke patients with aphasia. Have the therapist to educate loved ones or family members on how to perform exercises and practices to stroke patients. The more you do the better outcome... Also ask the therapist about the prognosis on specific type of aphasia.