Folder Library ''My Document'' view probem with share

I made a new view in a Folder library. This view ''My Document'' have limited permission ''Create by [Me] and Share with [Me]'' (photo no.1). This view now is select as default.

I have deleted the "All View" option. I do not want all people to see all the files.

The problem is when someone shares a folder, the recipient normally sees the folder but does not see the files inside.

Is there a way when sharing a folder to select the files in it so that they are shared with the person to whom you are sending them?

If I make a public view, the problem is solved, but I do not need all the people who see all the folders and files.

Thanks in advance,

Angelos