Adding non-Apple Store eBook to iPhone I have a number of eBooks (ePub) either from free sources such as Gutenberg, or purchased elsewhere.

I can open them easily enough on my iMac with eBooks, and I gather that they are in my library (when I try to add one manually, it tells me that it’s already there).

On my iPhone, however, I can’t see them at all.

How do I complete the processes?

I will readily consider a third party app.

I have the latest version of all software. In particular, iTunes 12.7, which is of no help to me at all.
The only way to get those books on your iPhone is to open them on the phone. My recommendation is to upload all of those books to a cloud drive, then download them from the drive and then open them via iBooks.