Lithium batteries while towing RV

I currently tow a small RV trailer with battery "on" while towing my camper. Has anyone found that this actually damages the alternator in the truck? I do this to run the refrigerator during travel. My camper battery is lithium and made by Renogy. I've heard some people claiming this damages the trucks alternator. Curious if anyone has comment on this. Thanks

 

It is my understanding that the issues with alternator damage occur when using a lithium battery as the starter battery for the truck. The damage will occur when the BMS disconnects the battery from the alternator when it is full. Again, this only happens when you replace your starting battery with a lithium one that is not designed to replace a lead acid starting battery. Your application should not cause damage to the alternator.