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"I named my son after Santino Corleone in the Godfather and the man who infamously played him passed away today on my son's birthday," he captioned a side-by-side photo of Caan in the iconic film and his son looking at the camera with pursed lips.
"From one Sonny to another… God bless you James Caan & Happy Birthday Sonny!"
The post also included a more recent photo of Caan posing with Lopez.
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James Caan died at 82 years old, a tweet from the actor's official account Thursday announced. A cause of death was not made immediately available.
"It is with great sadness that we inform you of the passing of Jimmy on the evening of July 6," the statement read.
"The family appreciates the outpouring of love and heartfelt condolences and asks that you continue to respect their privacy during this difficult time," the tweet added.
In addition to Santino, who family and friends also call Sonny, Lopez is dad to daughter Gia Francesca, 11, and son Dominic Luciano, 8. Wife Courtney Lopez also shared a birthday tribute to the youngest of the couple's three kids.
"My baby turned 3 today. Crazy how time flies," she captioned a set of photos of their son throughout the years, starting with one where baby Santino is dressed up as Woody from Toy Story.