But typically, you don't need to prove that you bought something if you can prove that you own it. If you have title to a car, you shouldn't need the bill of sale.
Having the physical share certificates in his possession is akin to having title. Without evidence questioning the title, there is no justification to shift the burden onto him to prove that he purchased them. Sharp would need to provide evidence that linked Calasse to O'Flynn prior to the stock transfer agreement, or in some way undermine his valid ownership in the shares.
If Sharp did that, then I agree that the court might require Calasse to prove that he purchased the shares. But without any evidence from Sharp, I don't think the court will even entertain this argument.
If someone can't tell that a shell is a shell, can you trust anything else that they say?