Greaves started playing with her older brother Taylor, who had a dartboard in his bedroom, and quickly showed her aptitude for the game.
“When she was 11 she went to Jersey with her mum and I remember her beating top women’s player Lisa Ashton and me,” Hedman told BBC Sport.
“Even then, I knew she was someone very special.”
Hedman was the first woman to beat a man in a televised major when she defeated Aaron Turner in the 2005 UK Open and says Greaves can compete at the highest level.
“I do believe Beau will do some damage. Some men do not like playing women even in this day and age as there’s more pressure,” she said.
“Whether she will ever win one of the big majors remains to be seen. She has the game to beat them.
“And she’s such a sweet down-to-earth lady from a lovely family. You couldn’t find a nicer young person.
“Within darts there is always going to be back-biting, jealousies but what you see from Beau is what you get and she has time for everyone, whoever you are.”
World number one Humphries has been among those to praise Greaves, who made history in February as the first woman to reach the fourth round of the UK Open where she led him 7-5 before eventually losing 10-7.
“I think she’s an amazing player and she deserves it,” Humphries said during his run to Sunday’s World Grand Prix final. “I predict that she’ll flourish playing in it [PDC Pro Tour].
“She’s been a really great player on the secondary tours this year. She’s good on the challenge tour, good on the development tour and she’ll be a real threat going forward for all the players. Not just for me but for everyone.
“I think she’ll do really well. If she’s relaxed and she’s got no pressure on her shoulders yes, I believe she will be top 64 within the two years for sure.”
Greaves will face defending champion Gian van Veen of the Netherlands in the youth final at Minehead in November.
The next instalment of Greaves v Littler could potentially come as early as next month too at the Grand Slam in Wolverhampton.
And then who knows? She could become the second woman after Fallon Sherrock, in 2019, to win matches in the big one at the Ally Pally.
