Problem with moving photos to new album on iPhone
Albums on Photos are not like folders or "real world" albums, where you would put a copy of your picture and empty the "box" where they came all together.
They work like tags, where you would mark a picture with the themes it pertains to and when looking the album you're just organizing by tags ("family trip to Chile", but also "In laws", "Summer"); if you erase your pictures from the camera roll (the "box"), they get erased from every album because you're deleting the original which is "tagged" to appear on your albums.  

On the other hand, you can put the same image on as many albums as you like, without duplicating the picture, thus saving space.