How do I deselect Camera Roll when transferring from album to album?

Hi, I'm trying to transfer photos from an iPhone 4S to an iPhone 5S. I don't have any problems with the transfer itself, but ...

Say I have an album on the 4s called Pets. I create a new album on the 5s also called Pets. I start the transfer process, and on the 5s I make sure to select the new Pets album. I also see that Camera Roll and Photo Stream are selected, but I can't deselect them.

I transfer the photos, but in my 5s Photos app, they appear not only in the Pets album, but also in the Camera Roll, and the Photo Stream. I only want the photos in the Pets album.

If I try to delete the photos from the Camera Roll, it also deletes them from the Pets album.

I'm not sure if this is a problem with the app, or maybe some other settings, but I've looked around and can't see any settings that look related.

Can somebody help me with this?

Thanks! :)