Last month the boy's parents issued an emotional appeal for the return of the computer which had been used at the service to show photos of the little boy, TJ Martin, during the service.
It was taken from Pentecostal City Church in north London while his parents were at the burial ceremony close by.
Pat Martin, the boy's mother, said: "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."
TJ was born in Candle syndrome, a disorder characterised by inflammation and fever, and spent much of his life in hospital before losing his battle.
Norris Martin, 34, 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."
TJ's father left the laptop in a bag in church while the family went to the burial in Kensal Rise, around a mile away from the church.
Scotland Yard have said a man has been arrested and charged with burglary on Saturday.
Police issued a man's description in November and asked people to come forward.
Franklyn Mathurin, 47, of no fixed address, appeared at Hendon Magistrates' Court on Monday.
He will appear in custody for a case management hearing on December 14th.
