Basically, the problem was the architecture : UE4 is not made for manual replication, I mean, passing pointers as function parameters in order to store them.
The right way to do an inventory system was to replicate CurrentWeapon and Inventory, with an OnRep. Manual replication is not the “UE4 way” to do this. So, I corrected my mistakes, and then, it worked !
I got this idea when I saw the ShooterProject’s source code, and I think it’s a great ressource for learning !