Mozaffar Saberi, 83, and his wife Rezvan Habibimarand, 73, settled in Bruntsfield in 1978 after fleeing political strife in Iran.
But the couple never sought citizenship and now face a final appeal against their deportation on February 25 over a visa issue - despite their 11 grandchildren being born in the Capital.
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More than 120,000 people have signed an online petition calling for home office officials to overturn their “shameful and heartless” decision and Edinburgh Rugby star Hoyland, 25, is hoping public pressure can help change their minds.
He told the Evening News: “If they are sent back to Iran, it will tear my family apart, quite simply we will never see them again.”
“I don’t know who sits at a computer and comes up with these decisions, but if this happens, there will be no going back for me or my family - I’m just not sure how we will cope.”
Mozaffar and Rezvan moved to the Capital from Tehran after violent clashes in the city at the start of the Iranian revolution.
Dentist Mozaffar attended the University of Edinburgh where he continued his postgraduate studies, but the couple made frequent trips back to Iran to visit family members.
They have remained in the UK on visitor visas over the years, but in November 2012, Rezvan’s declining health persuaded the couple to stay permanently in Scotland, where they now have one great-grandchild.
An initial application to remain in Edinburgh on human rights grounds was refused by the Home Office, while a second appeal was also turned down.
Damien recalled visiting his grandparents in the Iranian capital as a youngster, though admitted he had “virtually no memory” of the trip.
But he does remember large family gatherings in their Bruntsfield flat, adding the couple had been a “constant presence” in his life.
“When I look at them, I don’t see immigrants, I see an elderly couple who have been back and forth to Iran, but have always had their roots in Scotland, who see their home as Scotland,” Damien said.
“When they moved here, they brought my mum across, they moved almost their entire life here and I think they realised it was a great place, it was where they wanted to be.
“As a family, we all contribute to society in so many different ways, my brother is a teacher, my mum was a nurse, there is so much we have contributed, so to be facing this now, it is simply nonsensical.”
Damien added that his grandparents act as co-parents for one of their grandchildren, a teenager with severe autism who does not speak and requires constant supervision.
Their help means the boy’s mother, Damien’s aunt Ladan, can continue her work as an NHS nurse.
But he admitted he is “extremely worried” about the potential impact on Ladan if the appeal is unsuccessful.
“It would just absolutely destroy my cousin, he isn’t comfortable around many people, but they are always so calm with him, he is happy in their company,” he said.
“My auntie Ladan would have to quit her job as a nurse, that detriments the NHS, to look after him, which means she would be claiming benefits, so she would be taking money off the state.”
“You start asking yourself, what benefit are they going to get from deporting them? The only reason they have to do that is to cause distress among our family.”
Damien is hopeful the entire family can attend the hearing next month, but the four-time Scotland cap admits he faces an anxious wait to learn his own fixture schedule so that he can lend his support.
He also thanked the public for their support, adding the family had been “overwhelmed” by their backing.
“I want to be there, obviously. We all do, hopefully I can be there with my family and the correct decision is made.”
“The positivity we have felt from everyone who has signed the petition, everyone who has supported us has just been phenomenal. I can’t thank everyone enough.
“These are just normal people who realise this is simply an immoral decision, that is why my grandparents came here in the first place, because of that welcome, that positivity.
“It is clear what the moral decision is here, I just hope it is made.”