Replika will have many ethical problems as you can "talk to the dead". I'm interested to know how they are going to manage that. Also, I don't really like the idea that an AI mimics me 
From my understanding is that they, and other companies like them (they're not the first to do / attempt this), basically take as much recorded or information from notes, other texts, eye-witness and close friends and relatives on what that person liked and disliked, his / her belief system if any, sports interests, favorite teams, colors, cars, drinks (beer, wine, mixed, soda, etc.), what he / she looked for in a person, facts about their education, family life, vacation spots, etc.
They set out to collect as much information as they could possibly obtain then that data is compiled into a useful format befitting a database of that person's life, from birth, school, military service if applicable, marriage, children, work, retirement, death...or something along those lines.
Once this program is able to use decent conversational flow, it can access the database and now field and answer questions from people (friends relatives, spouses, etc.) and it would give that person as real an answer as if the (deceased) person was typing (or speaking) it themselves.
Almost a brain in a box but really it's more of a database in a box with memories of that person while he / she was living. It cannot think on it's own not can it obtain fresh input or deliver new output except what is contained in the database.
While very interesting and entertaining, it is certainly no substitute for the real person, but having said that, it might certainly provide a needed purpose, a measure of relief for those in morning or grieving the loss of a loved one. I judge no one in this regard having just lost my father in Jan. and my mother in April of this year, less than 3 months apart.
I found one last voice message my mom left on my phone a day before she passed away and she sounded so happy. I never got to say goodbye to her. How I'd love to be able to talk with her again.
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As far as the joke about the A.I. that mimics you, I don't think you'd be in a position to have a say in the matter at that time. Just saying... but I understand what you're implying.
