A laptop used to show photographs of a six-year-old boy during his funeral was stolen from the church as he was buried nearby, Metropolitan Police have said.
The theft of the computer took place after the funeral service for Norris Tashan-Javan Martin, known as TJ.
His mother, Pat Martin, said the laptop held "all their memories" of TJ.
Reverend Desmond Hall, pastor of Pentecostal City Mission Church in Willesden, north-west London, said the thief was "masquerading as a mourner".
The incident happened on 2 November.
Mrs Martin 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.
"It doesn't mean anything to the person that's got the laptop. We just want the memories - please. If you don't want to be identified, just give it to someone to hand in."
Rev Hall said TJ, who "always had a smile on his face", had been very ill for his whole life with Candle Syndrome, a rare disease that affects the immune system.
He said the congregation of more than 300 people included members of staff from the Great Ormond Street and Northwick Park hospitals, where he had been treated.
"It's traumatic for us," he said of the theft. "We are all stunned and asking how can anyone steal from the funeral of a little boy?"
The theft happened when the congregation left to attend the burial ceremony at nearby Kensal Green Cemetery.
Police said the suspect, aged about 40 with a distinctive limp, entered and stayed in the church for about 15 minutes before he was seen putting the laptop into a carrier bag and leaving.
CCTV footage showed him chatting with a receptionist before he entered the church hall on Scrubs Lane.