A 1,000 watt generator is really around 800 watts usually. I doubt it would handle a 45 amp charger.You need at least a 2,000 watt unit to run a 45 amp I would think. You could just pick up a 15 to 25 amp smart charger and connect it manually. I've used my 15 Amp Stanley charger with a small generator.
Open the door to your "breaker panel" or power center. Inside will be a label with the brand and model. Most RV's I've owned had the converter in the bottom of the power center box. I had one big 5th wheel with a separate converter wired to the power center, not sure why. The converter was mounted right behind the power center, I would expect to find it next to the batteries. But instead it was below the bathroom sink cabinet.
When your batteries are down to 12.40 volts, how fast do they charge? Whats the charging voltage? The WFCO converters I've had did okay plugged in for days at a time, but on generator power I never saw any of mine hit the 14.4 volt mode. On generator you want the "boost mode" for faster charging.
I prefer something like this in my rigs:
https://www.bestconverter.com/PD4655MBA-WildKat-55-Amp-Main-Board-Assembly-for-WFCO-8955-or-Parallax-7155-Includes-4600-Remote_p_616.htmlYou want the charge wizard pendent so you can manually control the boost mode. At least I do. The Boondocker version doesn't come with the pendant last I checked. I like the four stage wildkat or the name brand progressive dynamics converters with manual control pendant.
The last one I installed replaced a 8955 that charged at 13.23 volts, my WildKat converter starts out at 14.33 at the battery terminals. Then it drops down to the mid 13.50 range in auto mode. It does a good job, batteries get fully charged much quicker now. Healthy and fairly new batteries should rest at 12.70 or more when fully charged.
You can use a basic digital voltage meter at the converter and at the batteries to see how much drop there is in the cables. When testing the health of the converter, take your voltage reading at the converter's DC terminals.