Osborne was partnering the Alexandra Dunn-trained Zeyzoun in division one of the Follow At The Races On Twitter Handicap when her mount clipped heels with Maykir, sending the 7lb claiming apprentice out of the saddle.
The 18-year-old was then trampled on by horses following in her path.
Her father and trainer Jamie Osborne, a former National Hunt jockey, admitted he was relieved the damage was not much worse – given the nature of Monday’s incident.
And Osborne Jr communicated a similar message via social media.
"I haven't seen the fall and don't remember it," she said. "I feel very lucky to have escaped with only a broken arm, broken ribs and a puctured lung.
"I would like to thank the incredible doctors and paramedics at Windsor Racecourse as wella s the surgeons, doctors and paramedics at Wrexham Park Hospital for all the care and attention that have already put me on the road to recovery.
"The surgery of my arm has gone well and I'm looking forward to getting back in the saddle. See you all in the yard or on a racecourse soon."
Thank you to everyone, the incredible medical staff and The NHS! X pic.twitter.com/zraFWcl55I— saffie osborne (@OsborneSaffie) October 20, 2020
Osborne Sr had said earlier: "She’s got broken ribs, a little bit of potential trauma to the lung from the ribs – so they’ll monitor that, and hopefully it won’t need draining – but everything that is broken will mend, which is the important thing.
“Having watched and participated in many falls over the last 35 years, you kind of have a sense of when it’s not good – and watching that fall, it had the potential to be a not very good outcome.
“To be honest we’re all relieved that, while there are broken bones, they will mend – it could have been a lot worse.
“This year was all about her gaining as much experience as possible – so she’s experienced a little bit of everything now!
“She was going to go away this winter. We’ll put that on hold, and she’s got plenty of time to get better for the start of next season. It will take more than this to put her off.”
Osborne, an accomplished event rider, has ridden nine winners in her first season racing.
Marco Ghiani, the rider of Maykir, was handed a 10-day ban because of the incident.
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