Re: "AI becomes replica of son"
"simply titled A.I. Artificial Intelligence and mentioned briefly in the article."
No - not that one. The film I meant was much darker. An interactive AI mainframe super-computer is given access to the professor's home with webcams etc. It gradually takes on a malevolent character - interacting more and more with the still grieving mother and her memories of her dead son.
What it wants is to be a real living person - free from its hardware confines. Eventually it starts to make a cocoon to generate its new body. To stop it the power is disconnected. The film ends as the cocoon bursts open and a child emerges looking like the dead son - with the malevolent personality and powers of the super-computer.