I used to be able to save Facebook pictures to my device or to the wall using the Facebook app on my Samsung Galaxy Tab, but I can’t do this on my Galaxy s4. Why?
It may not be a feature offered for phones (my wife isn't able to do the same and uses a different app to post pictures as well as download Facebook pictures). Instead, you can use Friendcaster as there are more capabilities than the official app (it's what we use). The free version does contain ads, but they are small and unobtrusive, and if necessary, the ads can be closed individually.