Yes, the exporter will need to list the seeds at least to the genus level, but they prefer species. Then they have to include other things, such as the country of origin, who collected the seed, etc.
I just made a chart with the info that they need, and email it to the exporter, along with a COLOR copy of one of the shipping labels and the permit. Makes it really easy. I use it myself when I travel.
I also carry seed cleaning supplies, various little plastic baggies, desiccant and water beads, and addressed padded envelopes to mail the seeds home.
All carried around the world a zillion times in my "Happy Little Vegemite" lunch box!