When I get invited to a shared album, does it affect my internal storage?

Any photos that you saved or downloaded from a shared album to your Photos library stay in your library even if the shared album is deleted or the person who created it stops sharing it.

Save photos and videos from a shared album

When you share photos and videos with someone, they can save the shared items to their own library.

1. Select the photo and video that you want to save.
2. Control-click, then click Import.

The link, under “Related Article”, on top of this page says it all.