The couple arrived in Canada in February 2016 after fleeing war-torn Damascus.
Although photos of the charming encounter show Prime Minister Trudeau happily snuggling his young namesake, baby Justin Trudeau seemed a bit less impressed with the meeting. After learning Canada was starting to take in Syrian refugees after Mr Trudeau became Prime Minister, they jumped at the chance to leave.
Justin Trudeau says he has B.C.in his blood. They now call Calgary home.
Ms Hammoud told Canadian broadcaster CBC meeting the man who inspired her son's name and gave them their new life in Canada was an wonderful experience.
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"My husband says 'How about if we name the boy Justin-Trudeau, like him, '" she said. Between November 2015 and January 2017, the country has accepted over 40,000 refugees.
'It will be a big story because you know, the Arabic name and the English name, there is a big difference, ' she said.
Doso, a Syrian father in Red Deer, named his own son Justin. The family took refugee in Canada on February a year ago and their baby was born in Alberta, after few months.
Following US president Donald Trump's ban on immigration from seven Muslim-majority countries, Mr Trudeau wrote on social media that his government remained committed to helping "those fleeing persecution, terror & war".