The way I see it, the FFH 390CCA battery is being used to jump start something else that may have anything from a 500 to 875CCA battery which is low or dead.
The FFH battery is already undersized for the jump start, so your overloading the battery and maybe DC to DC converter. When the jumper cables are connected, the DC to DC converter is now charging the FFH and the other vehicle, 2 batteries. Can it safely handle it? I don't know.
If somebody accidentally reverses the jumper cables, who knows what will happen to the FFH, not likely to be a cheap fix.
And I don't know the price difference between a DC to DC on the FFH compared to an alternator on a regular car. But I do know, that your not likely to buy a DC converter from the local parts store like you can an alternator.
Just think its safer to use a portable booster pack. Some of the newer ones are quite small and will do the job.