What do I provide to an investor in my company to make the investor feel secure?

[MarkMarkov]

What is the name of your state (only U.S. law)?
New York
I have an investor that wants to put up capital for me to start a business. I have been in this business before, but this capital will allow me to operate on a much greater scale. A new entity will be established for the business.
One issue is that this investor is outside of the United States and does not plan to visit. How do I make the investor feel safe that they've invested in my company and hold rights to their capital? In other words, I don't want to tell her "just send me the money", I want her to have some document or certificate saying that she has invested in my company. In reality, she has little interest in the business and does not have a visa to the U.S., but I want to set this up correctly. I heard this is done by issuing shares, but I am not sure... can someone please advise on how to do this correctly? Tnx.