I do suspect that a phase-a-matic will fare poorly with a square-wave input, though I haven't ever worked through exactly what it would do to the output. The briefly-generated 3rd leg that's phase shifted by the capacitance in a static converter is already only a marginal substitute for a real 3rd leg - feeding it a square-wave input seems unlikely to make it better :-)
I'm also not entirely sure what the feedback from the 3-phase motor would do to the inverter. Effectively the 3-phase motor on the device becomes a rotary converter, and it will do its best to force the 180-degree phase difference on the 220V input, to assume a 120-degree phase difference. With real line power, this just does some strange things to the voltage and current relationships on the input lines, but I can imagine an inverter being somewhat offended.
However, given that we're talking about a 6.5KW generator in this case, it's probably not an inverter unit.
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