New York 1 said construction worker Diego Pillco admitted he strangled Shelly, 40, in her Manhattan apartment after she caught him snatching money out of her handbag.
He is due to be sentenced next month to 25 years in prison, the report said.
"It's incredibly bittersweet," actress Cheryl Hines said last April of promoting the film without Shelly.
"This is such a happy time because this movie is so beautiful and it's very exciting that people are noticing that ... and taking something away from this movie and, at the same time, Adrienne should be right here and it's not fair," Hines told UPI.
"I wish she could be here to hear people tell her and to see for herself how she has affected them," Fillion said. "What should have been one more piece in a long line of beautiful works has become a legacy and I'm very happy to have been a part of that."
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