Move files to different folders, but not right to delete

A new feature, perhaps?

I have shared a folder among some users and I have deactivate the "delete" action in Sharing, because I don't want to give the right to delete files/folders.

However, I think It would be a nice feature if the user could have the right to move the files to different folders (inside the share folder) but not able to delete any..

Yes, that would be a new feature and make the settings even more granular. Complex because we would need to check that the subfolder is shared with the same people and you might share the subfolder with others who aren't supposed to see this file ...
If you share a single file, then you have the effect, btw. as shares can be moved freely.

Keep in mind that often a move is a put and a delete, so depending on the client it will also be tough to trigger ...