When websites share image(s) via the share-menu, iOS prevents the user from saving the image(s) to Photos directly. It simply does not offer the option.

Demo of a website sharing images: https://benkaiser.github.io/web-share-images/

This simple shortcut bypasses that restriction, as it takes any images/videos from the share-menu and saves it to the album 'recents'.

UPDATE: Apparently, this was a bug and is fixed in recent iOS version (https://github.com/WebKit/WebKit/pull/13111)

Tipp:

Add this shortcut to favorites so it appears at the top in the share-menu:

1. open the share-menu from an image
2. go to the bottom of the share menu and tap on 'Edit actions...'
3. find this shortcut and click the green plus next to it
4. Tap 'done'

Guide with screenshots: https://www.iphonelife.com/content/how-to-rearrange-app-icons-share-tab

PairDrop

You‘re tired of AirDrop being restricted to Apple devices only?

Just use PairDrop instead

https://pairdrop.net/

Shortcut to PairDrop from Share Menu