In a letter released by the university, the family expresses thanks for the kindness they have been shown before and since they arrived in Canada last week.
"We are deeply touched by the kindness inspired by this human tragedy," the family statement says.
"It is our wish to take this opportunity to turn a devastating situation into something positive that brings the goodness and peace back to society."
"This tragic loss is not only a devastating attack to our family, but also has had a tremendous impact on the whole society. Love and trust must be rebuilt."
Lin, 33, was studying engineering and computer science at Concordia.
His dismembered torso was found in a suitcase outside a Montreal apartment building last month.
Lin's hands and feet were mailed to the Conservative and Liberal parties in Ottawa and two Vancouver schools.
Luka Rocco Magnotta, a 29-year-old porn actor and male escort, was arrested in Germany last week and is awaiting extradition back to Canada to face a first-degree murder charge in Lin's death.
The family says it wants the extradition to take place as soon as possible.
Concordia has taken several steps to keep Lin's memory alive amid the outpouring of public support for his family.
In the letter, the family notes an award will be named after Lin, along with a fund to help his relatives pay their expenses during their trip to Canada.
They also talk about Lin being a kind man.
"As the only son in the family, he was our pride and hope. Jun Lin believed in Buddhism. He was very kind and always enjoyed helping others."Suggest a correction