FWIW, I charge my batteries with 2 chargers, daily.
I have two LIFPO4 Batteries: https://amzn.to/3aGzrth
And I charge them with my solar panels through this: https://amzn.to/2TTMMsg
On cloudy days, I turn my propane powered generator on: https://amzn.to/30TcnCZ
And then use this charger to charge the batteries on cloudy days or when tied into shore power: https://amzn.to/37tAhrh
So the two chargers work together. Whichever is feeding the higher voltage is going to charge the battery. The BMS (Battery Management System) inside the battery is going to control the resistance the chargers are going to be able to work against getting their current to the chemistry so to speak.
The only thing I would be concerned about is charge rate in your setup. I would definitely get an amp meter and figure out how much current your converter is putting out. In an AGM battery, if you want it to last a long time, I would not charge it more than 1/3 C. Which might be like say 30 amps. Also, since you are using lead acid, I always recommend an automatic disconnect. If you discharge that battery less than 12.2 volts even one time, the process has begun for your battery to become nearly worthless. It will lose something like 50% of it's capactiy the first time you discharge it less than half. Something like this installed will prevent that from happening: https://amzn.to/2TVVztR
If you have more than 100 amp battery you can charge at something like 40 amps, it's not ideal, but you can do it (even 2 chargers at once).