At any point while you are working in the hypothetical illustration tool, you can save your work.
Click Save. The first time you save a new illustration, you'll be prompted to name it, but after that, clicking the save button will just save it without requiring any more action on your part.
Click Save As. Any time you click Save As, you'll be prompted to name the file.
When you open the file later, all of your saved inputs (including your investment selections) appear.