I cannot see this as being helpful to the grieving process. I do see it being useful for businesses: create a chat or VR bot of a founder or shrewd executive to tap their take on things on demand. This is similar to the ghost AIs in Cyberpunk 2020, and to the corporate ghosts in the Cat series by Joan D. Vinge.
Anyway. I'd want to come back as Clippy.
I do not believe we will ever capture emotion perfectly in synthetic life. I think they will be capable of feeling, just not the way we do. As a result, I think Art will be an area where humans will still dominate. More specifically, our forms of Art. Since I believe they will eventually be able to feel, but not the way we do, it stands to reason that they'll have Art forms but ones that are greatly different from ours.
Business management is mostly a science based on 95% logic, 5% intuition, and that intuition is more subconscious hyper-logic than emotion. To me that means an AGI trained from the personality and thoughts of a business leader should be able to make similar (if not the same) decisions as what the business leader would have in life. I think V-space clones like Zoe, except for business, will be a thing for this reason.