Collina said she told her son, "At this point you should be ideal".
He was born in the Moroccan city of Fez in 1995.
Delcros was seriously injured by the van, although her condition in hospital has stabilised, her family said.
"It is a disgusting thing, something that should not happen", she said. It's something that should never happen.
Zaghba was said to have been placed on a watch list by Italian authorities and flagged to their Moroccan and British counterparts, but a lack of evidence about his intentions meant his phone and passport were returned, Italian media reported.
He was travelling alone and with only a small amount of luggage on a one way ticket to Istanbul, and police believed his final destination was Syria.
The Metropolitan Police opened a casualty bureau for those anxious about the whereabouts of people they know. Ho said "their eyes were full of rage", and he feared they were about to blow themselves up. I said "yes, absolutely".
The Metropolitan Police said all of the 15 victims now in critical care had been identified, as public appeals continued for several people who have not been located since the attack.
Giuseppe Amato, the Italian prosecutor who investigated Zaghba told me that he was considered a sympathiser, rather than someone who had committed an offence.
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He was one of about 3,000 suspects who were known to British authorities but not part of 500 active investigations. Zaghba's Italian citizenship prevented such an expulsion, Italian daily Repubblica said.
"I'm calling on all Londoners to pull together, and send a clear message around the world that our city will never be divided by these ugly individuals who seek to harm us and destroy our way of life", Khan said.
She died in her fiance's arms after being struck by the speeding van on London Bridge.
Relatives of Australian Sara Zelenak have confirmed she was another of the victims of the weekend attack.
Their condemnation came as footage emerged online appearing to show the moment armed police gunned down the three knife-wielding terrorists.
She added that police told her they were unable to formally identify him until the coroner's report is released.
Charisse O'Leary said she has "shed many tears for the people caught up in this horrific incident".
Seated cross-legged on cushions on the floor of her modest Bologna home, her head veiled, Collina said her last phone conversation with her son was "sweet".
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