If you are using a 2009 and UP F series FORD truck the TRAILER TOW DC VOLTAGE is controlled by a FUSE and a BLACK PLUG-IN RELAY in the truck fuse panel.
Look in the FORD TRUCK MANUAL for these two positions in the fuse panel.
My new 2010 F150 Truck had these two items in an unmarked envelope in the truck glove box. Apparently this only allows the TRAILER TOW DC VOLTAGE to be "ON" when the truck ignition key is turned on.
I don't know about the other brand trucks.
You mention INVERTER above - I assume you mean CONVERTER/CHARGER. This should not have anything to do with your truck not sending 12VDC to trailer when the truck ignition key is turned on.
You should read the 12VDC from BLADE 1 (GND) and BLADE 4(12VDC) at the truck 7-way receptacle whne the ignition key is turned on.
On your trailer side the 7-way TRAILER PLUG BLADE 4 should be directly connected to your trailer battery POSITIVE 12VDC terminal. There may an in-line fuse there as well.
sample photos from google images.
The wire colors shown on these two photos sometimes differ from the different manufacturers.
I would look around where the Converter/Charger unit ground connections were made - the warrenty replacement may have left some wires off near the battery terminals...
I assume all of this worked before TRAILER TOW 12VDC wise before the converter/charger was repaired.
BTW Most of us usually has an entry on what we are using Truck and Trailer wise either listed with the post or at least in our profile. Lets everyone know what equipment we have.