use calibre companion as the go between is what I do.
CC on my android tablet connects to calibre content server if calibre PC is on, or to dropbox backup if that PC is asleep. downloads books to tablet.
Moon + is configured to check the same CC folder in moon: My files preferences, or I open a new book once from in CC with Moon as the default reader gets the book into moon. ( moon does not re-copy the actual book, it just creates a database entry )
CC is v cheap but if all you want to do is transfer a couple of books each time then delete them after reading, the demo version is all you'd need.
to remove finished books I first delete the entries in Moon recents & bookmarks , but untick delete the file; then I go delete the file in CC. This keeps things tidy, with no orphan entries
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