It states that it is "PMA approved" - what does this mean and what is

required to get such an approval?

It means that a federal bureaucrat has decided that the design and
manufacturing system meet FAA standards, and thus the part can be sold
as an aircraft component.

Since the FAA standards are a bad joke, it doesn't mean the design and
manufacturing system are actually adequate.

The best (but not legal) solution would be to save the box, and to have
someone with a clue build you a real inverter (it's not hard) and then
seal the box up again.

Michael