How can Server control the item that a Client has?

Try this,
In your Character BP Event Graph,
Remove nodes that check authority (Switch Has Authority).

The client don’t have a authority so when the client has the Cap the authority check can’t be passed.

How about move these autority check node to
Event ‘KeyNexPic’ and ‘KeyPrePic’ in ‘BP_Cap1’ ?

Because some changes are really happened in there.