Different people are good at different things. There is no way to tell how long (or many whatevers) it takes for a specific person to learn something. With learning to write userstories itIt is no different with learning to write user stories.
If the PO has a hidden talent as an author or a blogger, he will catch up pretty fast. If he has a tendency to be very structured, he might never get it, because he might never grow above the "as a ... I can ... so that ..."
On top of that, learning something new not only takes practise, but also time. So if I answered: "It takes 1000 stories", it is of no use to lock him up in a cellar, to write the first 1000 stories. New things need time to sink in (a bit like: it takes one mother 9 months for 1 baby, how long do 9 mothers need?)
The 3. and I think the most important factor is real-life feedback. If the PO is constantly hanging out with the team, he will get direct and indirect feedback for his stories every standup. If this is handled equaliyequally well in retro your PO might write good stories for this particular project and team in 2 to 3 sprints.
So there's your answer: 3 sprints.
Question: how good are the feedback skills of your team and scrum master?
