Before going down the sync path, be sure everyone has read and comprehended this article. It’s honestly pretty logical, basic, and universally applicable—but it’s one thing to accidentally both edit one .docx file (and clean up the mess), and quite another to both accidentally edit a project format that can involve hundreds of them. While the info may be useful for all kinds of work, with databases and more complex multi-file formats such as Scrivener’s, it’s much more important to follow good sync practices (which again are honestly as dirt basic as “don’t unplug your computer while it is copying to the thumb drive” levels of logic, but you wouldn’t believe how many errors we see from doing just that, once the “wires” are invisible people get careless).
If sharing a project using live sync is not viable (scheduling means you both are sometimes on at the same time), then have a look at §5.3.2, Splitting & Merging Projects, in the user manual PDF. The subheadings I would look at in there are, Merging Changes from One Project to Another, and Collaborating with the Import Project Feature.
This describes a method that could be used to save a copy of the project into your share folder for your partner. Periodically they can let you know when they’ve reached a stopping point in the editing, and at that point you can import their “satellite project” into yours, merging the changes directly into it. You would then delete their satellite copy and create a new fresh one from the recently merged master copy.
For this, I would recommend using the File ▸ Back Up ▸ Back Up To... command, with Zip compression disabled. Key thing is that you can run that at any time to spawn a fresh copy of the project you’re working on without closing it or switching around confusingly, as Save As does. More importantly, it puts a date stamp on the file name, which could reduce sync related clashes when rapidly deleting and creating folders of the same name, and it will also help keep everyone on the same page. If your partner asks for an updated copy, and later that day a project pops up in the folder with today’s date, you barely even need to communicate about it.
Once get all of the details hammered out and the process learned, it’s honestly something that would take about five minutes of your time every now and then—and it means peace of mind and being able to work at your own pace and schedule, like you do now. Two people working off of the same project is always going to be more of an ongoing headache than periodically merging updates together into one master project.
You will need to be the one doing it for now though. The Windows developers have not yet added this feature.