The family had been planning a trip on the Titan submersible for some time, Dawood told the BBC in her first interview since the tragedy, but it was postponed by the Covid-19 pandemic.
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She had originally planned to make the trip with her husband because Suleman was too young at the time.
"Then I stepped back and gave the space to Suleman because he really wanted to go," Dawood said.
"I was really happy for them because both of them, they really wanted to do that for a very long time," she added.
Asked how she felt now about her son taking her place on the submersible, Dawood declined to say.
She also told the BBC that the 19-year-old was a Rubik's Cube obsessive who took the puzzle, which he could solve in 12 seconds, with him on the Titan.
"Suleman did not go anywhere without his Rubik's cube," Dawood said.
"He said, 'I'm going to solve the Rubik's Cube 3,700 meters below sea at the Titanic,'" she added.
"He was so excited about this," Dawood said, describing how Suleman taught himself to solve the puzzle using YouTube videos.
Dawood also spoke of how she met husband Shahzada at university, and recalled how his great curiosity about the world meant he would make the family watch documentaries together.
SEE ALSO: US Coast Guard will lead investigation of Titan implosion with help from Canada, France, UK
"He had this ability of childlike excitement," she said.
The above video is from a related report.
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Dawood recounted the moment that those on board the Polar Prince support vessel - including herself and her 17-year-old daughter, Alina - were told that staff were no longer able to communicate with the Titan.
"I didn't comprehend at that moment what that meant - and then it just went downhill from there," she said
Everyone thought the submersible would resurface, Dawood added.
"There was a lot of hope," she said.
"I think I lost hope when we passed the 96 hours mark," Dawood said, adding that at that point she messaged her family.
"I said: 'I'm preparing for the worst.' That's when I lost hope," she said.
As for what happens now, Dawood said she doubted she and Alina would ever be able to find closure.
RELATED: Families of Titan passengers may be able to sue despite possible waivers: Experts
"Is there such a thing? I don't know," she said.
However, the pair have vowed to learn to solve the Rubik's Cube, she added.
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"We promised ourselves we're going to learn it for Suleman," said Dawood.
The family will also work to continue Shahzada's work.
"He was involved in so many things, he helped so many people and I think I really want to continue that legacy and give him that platform... It's quite important for my daughter as well," she said.
"I miss them," she added. "I really, really miss them."
ALSO SEE: Suburban man took trip to Titanic wreckage on OceanGate's Titan submersible with CEO Stockton Rush
The Dawoods are from a prominent Pakistani business family.
Dawood Hercules Corp., their business, is among the largest companies in the country, with a portfolio spanning energy, petrochemicals, fertilizers, information technology and food and agriculture.
Shahzada and Suleman joined a voyage on board the Titan submersible - roughly the size of a minivan - to observe the wreck of the Titanic ocean liner, which lies around 12,500 feet below the surface of the North Atlantic.
SEE MORE: Missing Titanic submersible: CEO of company leading expedition, billionaire adventurer on board
The submersible went missing on June 18, about 1 hour and 45 minutes into its descent to explore the wreckage. On Thursday, debris from the sub was found by search teams, indicating that the vessel had suffered a catastrophic implosion, killing all five people on board.
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