Hmmm, if you want to pursue this, one method would be to run a temporary long extension cord from your apartment to his. Connect his TV gear and refrigerator.

Then make note of the electric meter reading and the time, then wait. See if his meter reading advances despite there being almost (or genuinely no) load inside the apartment.

You might have to monitor it for a while (overnight or a few days) if the pirate electrical load from some other apartment only occurs when that resident is home, or cooking, or whatever.

Or put everything onto the extension cord, then pull the meter or turn off the service panel for that meter. Then see what complaints arise from the other residents.

You might even discover it is your own apartment that is benefiting from his meter.