I've plugged the AC charger for my Samsung Galaxy S4 into an inverter connected to my car's DC outlet. The inverter is able to power my laptop AC adapter without issues. The S4 charges, but not at full amperage.
The app Ampere shows that power input is at or below 500mA instead of the 1200mA shown when the adapter is connected to a wall socket. Charging happens at a rate comparable to what is shown by Ampere, and similar to that seen when the phone is connected to a USB port on a computer.
Does Android or the Galaxy S4 refuse to allow charging at over 500mA if the quality of current is different from what would be provided by a wall socket?