I agree, Google Drive would be ideal and ought to work, but with Google being Google, sometimes things don't work as smoothly as they should.
I might have missed something earlier -- are you saying your wife is adding the screenshots to Google Drive on her PC? If so, is she uploading them directly to Google Drive using the website, or is she saving them to a physical folder on the PC's hard drive, and relying on Google's Backup & Sync program to automatically sync the file to the Google Drive folder in the cloud? If it's the latter, then I've also noticed that Backup & Sync doesn't seem to sync the file right away. I'm not sure how long it takes for the sync to occur, but when I look at it again a few hours later, it's finally synced.