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Midfielder Eriksen collapsed and suffered a cardiac arrest in their opening Group B game against Finland, but survived after being administered CPR on the pitch in Copenhagen and is now recovering after being fitted with a heart starter device.
Denmark lost that opener against Finland as well as the next game against Belgium, but squeezed into the knockout stages thanks to a 4-1 drubbing of Russia.
Roared on by their fans in Amsterdam's Johan Cruyff Arena on Saturday, the Danes blew away Wales with two goals from Kasper Dolberg and one apiece by Joakim Maehle and Martin Braithwaite securing a 4-0 win and a place in the last eight of the competition.
"When Christian collapsed, that's when everything changed for me," Hjumland told a news conference.
"I felt we were put in a totally different situation.
“We are grateful for all the love and support everyone has shown because it gave us wings, and being in the quarter-finals is amazing.
"Knowing that this ground was Christian's first home after leaving Denmark, I would have loved for him to have been here with us today but I know that he is with us anyway."
Eriksen played for Ajax from 2010 to 2013, and Dolberg - also a former Ajax product - enjoyed a dream return with a superb brace on his first start in the tournament.
"This is total madness. It's surreal. It was here it all started for me, and to play here again in this setting was insane. We dreamed about this and believed that we can get here," he said.
"This has always been a great team to be a part of and I felt I was in a special afternoon when I walked around the city and then into the stadium today."
Additional reporting by Reuters.