Are chatbots based on deceased loved ones healthy?
In my opinion, it depends on whether they would like the AI to synthesize novel thoughts/opinions or to merely contextually quote a history of that individual's textual recordings.

Making a value judgement here, I would say than an AI saying "I forgive you." (from beyond the grave) is not healthy.

But if the chatbot acted as a way of indexing into the individual's actual history, then all potential errors become ones of context (and not content).
(This level of reproduction may not be totally necessary depending on the users' sensitivity to cognitive dissonance, but I would personally feel slimy if I tried to pass off a markov chain of scripts and data as my friend.)

If you're open to alternatives to chatbots, I would suggest that you frame the project as a tribute to your friend's life; even a simple collection of stories from your time together could have a powerful (healthy) impact on the grieving parents.