I hard-wired my cell phone to the cigarette lighter wire with electrical tape and power wire. I just secured the wires to the phones cigarette plug and taped it up real good. I tapped into the cigarette wires by unplugging it and removing the plastic boots on the connection. Then I secured the power wire there and slipped the boots back on.
Not a professional job, but more than sufficient.
For you, using an inverter, I'd probably leave the cigarette lighter disconnected and just hook up the inverter. That way you won't over-heat the circuit.
My .02
Good luck...
