That's not a technical problem.
The inventory screen has two parts. Your actual inventory (backpack) and stuff on the ground/in a barrel/on a shelf. You can switch and transfer item between them using the two colored arrow icons on the screen. With the upturning/green arrow you can take items from the ground/barrel/shelf/etc. and with the downturning/yellow arrow you can put items from your inventory into the container/on the ground.
These two arrows can also be used to switch between the two inventory parts. So to put anything from your backback into a shelf, do the following: touch the shelf, touch the down/yellow arrow to switch to your backpack, select the item you want to put into the shelf, then touch the down/yellow arrow again (or just doubletap the item).
I, of course, freely admit it's not the most intuitive mechanic on first sight.
