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Yasmin and Mohammed Javed say they plan to make donations to appropriate charities because their daughter Fawziyah Javed was always helping people.
The couple, who live in Leeds, are also giving money to a range of organisations in their own area and abroad to reflect Fawziyah's wide-ranging care for others, but wanted to include Edinburgh in their generous gesture.
Fawziyah, 31, was on a short break to the Capital from her home in Pudsey when she died following an alleged incident on Arthur's Seat in September.
Mrs Javed said: "It's heartbreaking. The whole family is absolutely devastated. Our whole world has collapsed.
"She was an only child and she was just perfect in every way."
She said Fawziyah, who worked as an employment lawyer, had been involved with many charities, including ones working with the homeless, orphans, vulnerable young people and women and children.
"She was a humanitarian, she was kind, generous, wore her heart on her sleeve and was very giving and selfless. She had a good sense of humour and was loved by everybody.
"She would take time out to help people. She did a lot of volunteering, starting as a teenager and continuing right up until now. She did it all her life.
"And not only did she volunteer for charities, she also used to give a lot of money to different charities.
"My family and I want to donate to charities in Edinburgh as a tribute to Fawziyah.
“We wanted, as it's coming up to Christmas, to give some money to help homeless people or contribute to Christmas presents for children in hospital or hospice.
"We're doing things in other places as well – there are water wells going to be constructed around the world and we’re helping to feed some homeless people in Yorkshire as well.”
Mrs Javed said her daughter was pregnant with her first child when she died. She had also been due to start a new job at a different law firm the following week.
Fawziyah’s family found themselves having to identify her body on what would have been her birthday.
One of the charities where Fawziyah volunteered was the InTouch Foundation, which supports homeless men and women in Yorkshire.
Its chief executive Osman Gondal has paid tribute to her, saying: "Fawziyah was a kind, caring and compassionate individual that had an unprecedented drive to help those in need.
"She was a true community champion that was respected by both fellow volunteers and service users here at InTouch Foundation. I had the pleasure of working with Fawziyah and watching her flourish into a team leader.
“My thoughts go out to her mother, Yasmin, also a volunteer at InTouch. Their relationship was one to be admired as they always volunteered together.”
Fawziyah’s husband, Kashif Anwar, 27, was arrested following her death and has appeared at Edinburgh Sheriff Court charged with her murder.