How to measure the power consumption (security protocol)

Your setup in the picture looks OK. I assume that your Arduino is working perfectly this way?

What do you mean by "no result"?

You should set your meter to "200 mA" and connect your leads to COM and VmAOhms. Does your meter read 0 A? Try lowering the dial to "20 mA". What happens?

If your meter doesn't respond to any current measurement it could be because a fuse is blown. if so, check the fuse. You may also want to check the battery while you have the case open.