So I got the idea from the trash can...
http://imgur.com/c5tgOtIHow it could work:
When you open a chest "
tap & hold /click the Chest icon
The inventory will have green borderline to indicate that items are ready to be selected
The items that are pick can have a small check mark on the bottom right side...
And when you're ready to move them just "
double tap /click" chest icon to fill in all the empty spaces inside the chest.
Sorry for the title.. Couldn't think of anything better.