The mental health nurse died aged 48 in 2017 - five weeks after being diagnosed with an aggressive brain tumour.
The British Army reservist, who had completed two operational tours of Afghanistan, was "extremely fit and healthy" and his diagnosis came as a "huge shock", said Ms Sykes.
She won a scholarship to sixth form at the Duke of Edinburgh's former school in 2019 from its partner school, Samworth Church Academy in Mansfield, Nottinghamshire.
The funds will go to charity Brain Tumour Research, which says brain tumours kill more children and adults under the age of 40 than any other cancer.
Ms Sykes said: "He led a fantastically full life, even studying for a degree in fine art, while juggling his career as a frontline NHS worker.
"He exercised daily and was a vegetarian. His diagnosis with a grade-three brain tumour in April 2017 came as a huge shock.
"I was only 15 at the time and couldn't really comprehend what had happened. He'd become ill so quickly and declined rapidly.
"It took a huge toll on my mum. She and Paul were planning to get married.
"As a family, we are passionate about ensuring no other family has to experience the pain we have been through."
Ms Sykes' mother Samantha, also an NHS mental health nurse, and her elder brother Charlie were also devastated by the loss.
Joe Woollcott, community development manager at Brain Tumour Research, said: "We were so very sorry to learn about the tragic loss of Scarlett's stepfather, Paul.
"His story reminds us that brain tumours are indiscriminate, they can affect anyone at any time. Our condolences extend to Scarlett's mum and brother and all those who knew and loved Paul.
"What Scarlett has done in memory of her stepdad is truly inspiring."
The charity is calling for more investment for research into brain tumours, asking for a national annual spend of £35 million "to improve survival rates and patient outcomes in line with other cancers such as breast cancer and leukaemia".