NEC rules not withstanding, this is probably going to end poorly for the consumer, so make sure you cover your bases by letting him know that there is a high likelihood of premature failure of these appliances, unless the manufacturer has SPECIFICALLY designed them for use on 60Hz, either by putting in a switch or using an electronic controller what can accept any input. You don't want him coming after you later for the cost of replacing them because "you are a professional and should have warned him".
The problem with them "checking on line" is that if they did that from a server inside of the US, the target website server for the seller typically identifies the query as coming from the US, so it will only show them the products designed to work here. That explains why they said it told them 120V, but you are seeing 230V 50Hz. The reality is, by buying the appliances IN Europe and shipping them here, they will have purchased versions DESIGNED for EU voltages, not ours. By the way, they will also not be UL listed, which is not really your problem if they are plugged in, but if they start a fire later and the insurance company investigates, it may become a problem for them at that time. Some insurers will not cover damages caused by unlisted appliances.
So the primary problem is that any AC motors (i.e. refrigerator compressors, washer motors, dryer motors, oven and stove fan motors etc.) will prematurely fail even if you correct the voltage. AC motors must get the proper ratio of voltage and frequency to provide rated torque and run at rated current. A motor designed for 220V 50Hz is looking for 4.4 V/Hz. If you provide it with 240V 60Hz, the ratio is 4:1. the motor will spin faster, but provide LESS torque, which means they will end up with more slip and pull higher than rated current. They will either trip their overload protection (assuming it is there) and be a nuisance or burn out prematurely.
Stoves and ovens are likely designed for Line to Neutral 220V (the EU standard) and I have seen where they ground the Neutral INSIDE of the appliance, based on other EU wiring standards. If that's the case, 240V single phase here is Line to Line, so any internal grounded Neutral connections will be a dead ground fault. You may have to go through the internal wiring diagrams of the stoves and ovens to search out any of these issues BEFORE applying power. Make sure you cover the time this will take you.
Things with electronic power supplies MIGHT survive, but there is no guarantee and I think you owe it to them to let them know.
It never ceases to amaze me how (and why) people insist on moving large appliances to or from other countries without checking into the ramifications FIRST with a qualified electrical professional.