Lots of times it's a race to fill every slot after a class change because you want to complete the set and work on awakenings, upgrades and evolutions. Well what happens if you pick the wrong piece? Or if you get those Archangel Weapons from the Castle Siege? No sense in upgrading them all over again and that's where inheriting your gear will keep you right where you need to be at a few clicks of a button.
We are always in a scramble to get gear pieces after going through a class change and sometimes we will just equip whatever we can find. Inheriting will allow us to fix this issue once we find the correct gear piece we are looking for to complete our set. You will inherit all the upgrades, evolutions and stat upgrades you had on your original piece to this new one.
This has always had a lot of confusion around it. You will have to manually go into the Inherit menu and select the weapon you are wanting to transfer to your Ruined, Regular or Blessed Archangel Weapons.