Thanks! The app looks a bit iffy! I think that they all suffer from the fact that Facebook keeps updating their protocols and the app developers can't keep up with the changes.
I found a slightly newer one at: https://itunes.apple.com/us/app/photoloader-for-facebook/id409349136?mt=8
... but have not tried either yet.
The article was interesting. I usually upload at High Quality using Easy Photo Uploader on my Windows PC but I did not know about .PNGs
Replying, somewhat later, to my own query.
I found that the best current way to upload a photo that displays as a 2048 pixel photo in Facebook's full screen viewer (or is available as a subsequent 2048 pixel download from Facebook) is to simply use the Facebook mobile website - m.facebook.com - in Safari over WiFi rather than use any app.
The Facebook's own app does not currently do it and, as Facebook seems to regularly change its protocols, apps usually go out of date quickly.
In fact, I think the website, in Safari, is usually better than the app for most purposes and I see a lot of posts supporting that preference.