How Do I Move photos from "My Photos" to albums?

When you click on the "My Photos" tab you get the overall view of your album organisation, and at the very top you see "All Photos", which is the composite view of your entire collection of images in your cloud space. You cannot "move" images out of All Photos except by deleting them entirely from the cloud. You can of course organise subsets of images by adding them to albums (not folders), but they will still always be seen in All Photos as well (if you don't have All Photos, how can you see the images in order to organise them into albums, and what do you do if you need to filter or search across all your images?).

If you want to speed up loading of All Photos on your phone, you could consider downloading Smart Previews of them all, though of course that would likely take up a couple of GBs of space on the device. Easiest way to do that:

1. On the phone, open the main Settings menu, select the Cloud Storage & Sync tab, enable "Only Download Smart Previews".

2. On the phone, first create a new album, then select all photos by tapping on the three dots top right, tap on Select in the resulting menu, then select the All Photos option at the top of the next screen, then when all are selected tap on the "Add to" icon at the bottom of the screen. That display a list of all albums, tap on the one you have just created and all your images will be added to that album.

3. Go back to the main screen, where all your albums are listed, tap on the three dots alongside that new album and on the resulting screen enable the "Store Locally" option. That will begin to download a smart preview of your entire cloud library, when compolete that will result in much faster access to your images when you subsequently start the app on your phone.