Copying photos from shared album

Yes, the Shared albums are using separate copies of the shared photos. When you drag a photo from a Shared album to an album, it will be imported as a new photo. You can check, if it worked, by ctrl-clicking or right-clicking the photo in the shared album.

• If you are seeing the option "Show in Moments" the photo has been imported to your Photos Library. Click this option to see the imported version in the moments.
• If you are still seeing "Import" instead, click "Import" to save it to your Library. Then you should now be seeing "Show in Moments":

I sincerely hope the article below assists you:

https://support.apple.com/en-us/HT202786

You're welcome 😊