I agree with Tom. Unless the existing inverter is dual voltage, 120/240, it would be replaced by the new 240V inverter and become unnecessary and could be sold. The only other consideration I can think of is the 240/120 transformer. It's likely to be quite large and heavy to run the a/c, micro and other devices, so space and heat produced (ventilation) need to be addressed.Otherwise, I don't see why it wouldn't work.
Good points, Lou. The motors may not run at the correct speed and will certainly get hotter. There are motor/generators that would do the job, but now you're talking big bucks and a lot of weight. There are also solid state freq. converters, but they're pretty expensive too. In the long run, might it not be better to sell the big-ticket items while stateside and retrofit with the proper replacement units when he's back home? Just a thought :-\A modern converter like the Progressive Dynamics should work OK on 50 Hz power. A converter with a 60 Hz ferroresonant converter obviously won't. A 3 way refrigerator probably doesn't care since the only 120 volt component is a heating element. But I'd question the safety of running the 60 Hz motors and transformers in the microwave and air conditoner on 50 Hz power. It would be wise to ask the manufacturers whether or not their equipment can tolerate it.