Keep in mind, depending on the inverter model you choose, it may come equipped with the same charging technology as the Truecharge2 battery charger you mention. So there would be no need to purchase both an inverter and a battery charger. The inverter itself becomes the battery charger whenever 120-volts AC is available (generator or shore power). Do some investigating here first.
My question is what makes you think you may have to replace your existing inverter/charger? Be sure it was diagnosed correctly before replacing it.