How do I move a screenshot from recents to another folder?

All albums in the "Library" section of the sidebar (Photos, Media, etc) are only managed by the Photos.app. They are essentially smart albums based on all photos and videos in your library according to specific rules for these smart albums. "Recents" will always be showing all photos in your library, sorted by the oldest date added.

You can only remove items from the predefined smart albums by deleting them from your Photos Library entirely - everywhere.

If you need an album like "Recents" where you find the most recently imported items, but want to remove the items, that you have already added to an album, create your own smart albums "My Recents not in any Album".

• File > New Smart Album
• Add two rules, combined with "Match All":
  • Date added is in the last 10 Days
  • Album is not Any

This smart album will be showing all recently imported items, that have not yet been added to albums.

With your own smart albums you can easily find photos according to rules, and supplement the predefined albums created by photos, with albums according to your own needs.

Hi

In Photos you don't move pictures. They are all stored once, and once only in the library. When they appear in other places (eg recents, screenshots etc), you are only seeing a view selected from the library.

So you can drag a screenshot from recents into an album - but it will still show in recents, as well as the album. There will still only be one copy of the image though.

How long do photos stay in "Recent"?

As Leonie said - recents show all images in your library sorted by date added.

They stay in there forever.