The only way to prove to the customer would be to have him move back to the original space and test the plug, but what would be the point if he's happy leave him there versus moving them back...
Load test the plug to ensure that all of the connections are tight. The biggest reason of things to not work is a loose connection, and that could be on your end or on the customer's end. So load testing the plug would prove (at least to you) that your service is good. Voltage testing is not the same as load testing... You could read 120V on each leg but as soon as you introduce a load (fridge or A/C) the voltage could drop.
