Albums to Folders

On the iPhone you have to create albums right inside the folder where you want them to be.

But you don't have to rechoose the photos from scratch, to create the folder structure you want. Try this:

• Create the folder and album structure as you want it to be with empty albums as place holders, but do not yet delete your existing albums.
• Then add the photos from the existing albums to the new albums, for each existing album individually:
  • Open the existing album. Select all photos in this album together.
  • Then tap the circled three dots and use the command "Add to album". Select the new album from the list.
  • Check the new album, if the photos have been added, then delete the old album.

Yes, on a Mac. Apparently not on an iPhone. Reports of mixed success on iPad.

If your devices are connected through an iCloud Photos library, the additions you make on your Mac should propagate to your iPhone and/or iPad.