Emily Quinn, who is also a lecturer at Heriot-Watt University, presented the gift – made from grey and cream 100 per cent cashmere – to the couple during their visit to the university campus in Galashiels.
It features the words: “Mighty oaks from little acorns grow.”
“It’s amazing,” Ms Quinn said afterwards. “I really hope it gets used.” Asked what Prince Charles said when presented with the gift, she added: “This will go down well.”
The royal couple were at the campus to meet textile and design students and wool farmers. The duke, who was wearing a blue Hunting Stewart Modern kilt and a Royal Regiment of Scotland tie, is patron of the Campaign for Wool, which encourages wider use of British wool to support farmers.
Jim Mitchell, who farms Scottish black-face sheep at nearby St Mary’s Loch, said Prince Charles was very knowledgeable about the industry. “When we were introduced his immediate question was how did we suffer in the bad weather [in March]. I was quite unprepared, I didn’t expect him to show an interest in that,” he said.
“He went on to speak about different breeds of wool. He was very knowledgeable and had a huge grasp of the subject.”
Scottish farmers hope the Campaign for Wool will create a bigger market for their products. “It’s about finding different uses for wool,” Mr Mitchell said. “From carpets and fleece, down to finer wools for clothes manufacturers.
“At the moment it’s not getting a great price. We’re just breeding it to suit the sheep for the cold weather.”
The School of Textiles and Design department had been carefully prepared for the visit.
On the first floor student designers had hung their work up along aisles for the royals to view. The duchess, wearing a long, lime green dress, stopped to chat to less conventionally dressed Scott Bramley, 22, a fourth year textiles and design student.
He had a collection of baggy tie-dye jumpers on display, inspired by grunge and the 1980s.
Mr Bramley, who was wearing a blue blazer and buttoned-up shirt, with orange shorts, said: “She understood it was knitted straight away and was really interested in the colours and the way it was designed.”
On the third floor the royal couple were joined by Scottish Secretary Michael Moore in viewing several large looms. Hannah Camp, 22, a fourth-year student originally from the United States, showed them how the looms work. The duchess said: “I’m so glad it’s still going,”