I am going to guess that since your object UInventory starts with a U that you are inheriting from a UObject. If so, there is your problem. According to the UE4 docs, Actors replicate, but UObjects do not:
If you are using an Actor and not a UObject and it still does not work, make sure you are also properly marking the individual properties that you want to replicate with:
UPROPERTY(Replicated)
And of course make sure that you set bReplicates = true; in your constructor.