The basic process is:
Tell the customer you’ll check the truck and with the movers who did the job, then get back to them
Have whoever is in the truck check thoroughly in case lost item is there
Text movers and ask them to give you a quick call when they’re free
Get back to customer and let them know what you’ve found. If we haven’t turned it up, at this point you can say with some confidence that it’s likely to be at the pickup or dropoff address.
If you can't get through all steps before the end of your shift, hand it over to someone who is on later than you/working the following day, as it's very important we get back to the customer in cases like this - we don't want them thinking we're stealing their stuff!