Tips for shipping directly to FBA warehouses from suppliers in other countries?

We’ve previously been shipping all inventory to ourselves, then we create shipments to the various FBA warehouses in the Amazon marketplaces we sell into. We would like to start shipping directly to FBA warehouses in those markets in order to skip a step and make the logistics more efficient.

At this point we don’t know what we don’t know. So we were wondering if anyone in this great community has any tips, anything to watch out for, any Amazon programs that would be of interest, etc.

Any advice is much appreciated.