Moving pics from my library into folders on my IPhone 11.

I understand you want to be able, which photos you already have added to albums, thus want to remove them from the library. The only way to remove photos from the library without deleting them, is the hide button. But in the recent versions of iOS the hidden photos will also be hidden from the albums.

However, you could temporarily hide the photos after adding them to an album, and when you are done with organising the new photos in albums, unhide them again.

Or, if you are also using iCloud Photos, enable the Shared iCloud Photos Library and move all photos you have added to albums to the Shared Library. They will vanish from your personal Library view. set the toggle switch to Personal Library while distributing your photos, and back to "Both Libraries", when done with filling your albums.

I have described this in this user tip: Using the Shared iCloud Photos Library to have two separate libraries on all devices - Apple Community

Library is a view provided by Apple to show all of the pictures in your Photos Library in order of the capture date in the pictures' metadata. This can't be changed. This album always provides the same view so that, when something goes wrong or seems off, you (and we) can depend on it showing the same thing, and there's no chance that someone changed the order or removed pictures.

As razmee209 pointed out, pictures aren't exactly "in" an album. When you "put a picture into an album," its name is added to a list of pictures to display when the album is clicked. So two albums can both have the same picture name in their lists, and that picture will show up when you click either album, but there's only one picture-- it's just on multiple lists. And when you remove a picture from an album, its name remains in the lists of other albums, and the file still remains in your Library. But, if you delete a picture from the Library view (a view of all the pictures in your Library), then the image is removed from your Library entirely. (Well, it goes to Recently Deleted for a month so you can change your mind. Thankfully.)

So albums give a specific view of your pictures. The picture of "Aunt Ethel at the Grand Canyon" can be in the "Aunt Ethel" album with other pictures of Aunt Ethel, and it can also be in the "Grand Canyon"  album with pictures of other people at the Grand Canyon. Both albums are each pointing to a single file stored in the Photos Library. Using albums that can have whatever picture you want in the without being restricted by other albums is very powerful in organizing pictures.

Withsmile10 wrote: Wont duplicate photos take up more memory on your phone.

True duplicate files would take up more storage space, and there is a Duplicates Finder to help with that in the newer iOSs.

But you can view a second image in a second album without having a duplicate file. That's because albums aren't containers of files, they are lists of images. In Music, if you have the song "Imagine" on your Beatles playlist and it's also on your Inspiration playlist, then you don't have two different song files-- the same song is just listed on two playlists. That's exactly the same thing for pictures in albums for Photos.

iCloud, by the way, offers the ability to have all your pictures on your phone in smaller sizes to save storage space. The full sized images can be quickly loaded from iCloud Photos if you need to zoom in or edit. But mostly we look at the small screen, anyway, so keeping the full sized images in iCloud saves space-- pictures may take up as little as 1/10th the space, saving a lot!

BarbieLover wrote:

When I go back to my library and delete those pictures that I moved, it also deletes the pictures that I moved into the folders.

How do I prevent that?

You don't that is how it works, you're not physically moving the photos to a folder, the photos points back to the original location ie your camera roll.

Wont duplicate photos take up more memory on your phone. I’m limited on memory and prefer not to remove from easy access files to the cloud