Businesses and their owners have to be registered with the government, in Ontario I think it's still the Ministry of Consumer and Commercial Relations, but it's a few years since I had my business. You can do a title search, there are paralegals that specialize in title searches, this is not expensive and it is often done when someone wants to register a business like "Steve's Burgers" to make sure there isn't another business with the same name. Again, it's been a few years but I believe the search should cost less than $100.
Having a "share" of the business doesn't mean necessarily that he is making income off of it. Most small family businesses don't turn an actual profit, mom and pop pay themselves a salary, and the business itself runs at basically a break-even. They may have transfered a share to him but he isn't working or taking a salary, and it is simply ownership, which may be set up to make it easier to inherit the business or transfer it in full later when they retire. There are many possibilities and you need proof that he is actually taking income from the business.
The business needs to file it's own tax return and this will show any payments as salary and any net profit. Once you establish that he actually owns part of it, then the tax info is what you should request access to. There's not much more you can do unless you want to make some huge fraud allegation and demand a full scale audit.