It is possible to add multiple products to replenishment from the replenishment menu Inventory > operations > replenishment

If you would follow creating the route as @Lars Aam suggests 

Alternatively, just a push rule in the receiving WH would suffice.

Rule - As eg. —  Push from Inter-warehouse transit location to Japan WH/stock operation type Japan WH/ Receipt.

Now by creating an internal transfer manually from US WH to interwarehouse transit location, it would be possible to add desired products and qty to a transfer.

On validation of this transfer a receipt operation would be created in Japan WH.

The push rule would be limiting if you wish to do transfer both ways. You might want to create multiple transit locations. Eg US to Japan and Japan to US and set Push rules accordingly 

The process is to create an outbound delivery from the delivering warehouse and a goods receipt  in the receiving.

In the warehouse configuration you should find the Resupply from and the warehouse name.  This should be flagged.  It will automatic create a route with the name Supply From warehouse (Name).  The route have to rules:  1: Create a Outbound delivery from the shipping warehouse to a Transit location. 2. Create a goods receipt from Transit location in the receiving warehouse.

Process: Open the product. Make sure the route for supply from Warehouse xx is flagged in the inventory tab. Press replenish, set qty and the defined route to use.   Outbound delivery and receipt is created. 

There are possibilities to make the process more or less automatic by using reordering rules on the product.