Photo shop elements currently has no way of allowing users to save an album they have created ... what is the point of creating an album if you can neither save it on your desk top or share it with others.
What's your own definition of an 'album'? In the first Elements Organizer versions, 15 years ago, they used the word 'collection' to describe a way to organize a list of selected files in a given order. They continued to call that 'collections' later in Lightroom, but they changed the word 'collections' into 'albums' for Elements. Very bad naming in my view. So, Organizer albums are just like playlist for music. They are not copies of your originals, they are lists kept only in your catalog for organization purpose. They are saved in the catalog and always available. Just select an album before you want to export, print or share its contents. I recommend taking the time to read the online help about the organizer to better understand and use albums and other ways to group images. Saving on your desktop, a pen drive, your social media? Creating photobooks, videos or slideshows? Albums allow all kind of sharing but they are not copies of your imges, only special lists.