I've noted that the ground fault sensor/switch is very sensitive and will "trip" when used on many generators. It essentially measures the current going into and out of the charger and if it's not almost identical (possibly indicating a short) it'll trip.
If the generator's 240V neutral is being used as the "safety ground" (yikes!) or the SG in the generator output is just a wire connected to the generator chassis, this is to be expected.
Wikipedia: "A ground fault (earth fault) is any failure that allows unintended connection of power circuit conductors with the earth."
A GFCI sensor detects the presence of current flow in the safety-ground conductor (which in a US home ends up connected to earth via a long ground stake at the house power entry point.). But unless your generator has a thick cable from its chassis metal & output safety-ground connection to a stake driven deep into the ground (as my 30kW does), it has
no safety ground at all. If its 240V output was designed for the USA it
will have a neutral conductor, which is absolutely NOT a generator safety ground and should
never be treated as such in generator applications ! A GFCI sensor will see this floating 240V neutral - or any non-staked generator "ground", for that matter - as the nasty non-grounds they are, and a good GFCI should trip almost immediately.
In short, don't sweat the lack of a safety ground, as the vast majority of portable generators don't have one.
Ray