[AC Question]

I want my pictures/attachments to save to Gallery on my Samsung Galaxy S5 mobile phone, not to my device, as I cannot save them to my Gallery.
When they save in my device I cannot not move them to another app, like Gallery.

[Rukbat]

You can't save pictures to Gallery, because Gallery has no place to save pictures.

When you turn the phone on, a media scanner builds a database of all the media files on the phone (and the external SD card, if you have one). Gallery looks in that database to see what picture files that it can display you have, and it shows thumbnails of them. They can be stored anywhere, unless there's a file named .nomedia (note the leading dot) in the folder the picture is in or one above it. (That signals the media scanner to skip that folder.)