The computer belongs to Norris Martin and was taken during a service for his son, TJ Martin, who died aged 6 after fighting a rare illness.
It had been used during the funeral at the Pentecostal City Church in Harlesden, north-west London, to show photos of TJ.
Mourners left the church to attend the nearby Kensal Rise cemetery for the burial, but on their return they realised the laptop had been taken.
47-year-old Franklyn Mathurin, of no fixed abode, admitted the burglary in November last year, prior to his sentencing at Harrow Crown Court.
The theft of the laptop, which has still not been found, prompted an emotional appeal from TJ's family calling for it's return.
Norris Martin, the boy's father, said: "The photos on the laptop are six years of family photos, even from (TJ's) birth.
"All the memories that we have of him are on that laptop. We have a few on my phone, but that's only the last year and a half."
Spending much of his life in hospital, TJ was born with the rare disorder, Candle syndrome, which included inflammation and fever symptons.
Pat Martin, TJ's mother, added: "It's as important as life itself that we get the laptop back.
"Unfortunately, TJ's life is no longer, he's been taken from us, and that laptop has all of our memories of him, short of what we hold in our hearts."