LCD display wrong chars with different power supplies

Hi guys,

I've tried to look for a solution on this forum but I was no lucky.

I've created a project based on this:

Code:

Links (except for power supply):

If I connect thru USB port, everything works fine (Setup chars + main chars)
If I connect thru power jack, there is the issue (Setup chars are ok, main chars are wrong)

Here attached pictures from both cases.
As you can see "Search & destroy" is shown in a proper way one time and in a wrong way if I change power supply.

Any hints on that?

I suspect that your 9V battery doesn't supply enough current needed.