I work for a client that produces a similar product here in Brazil and for them, exporting to the US is living the dream. The exchange rate is fabulous, highest prices in the market, and especially since Covid wood is in short supply (partly due to shipping problems that are still having an impact a year and a half later).
I do regularly see more exotic overseas hardwood in some lumber stores that specialize in catering to woodworkers, cabinet making, etc. Does your client specialize in these exotic hardwoods or is it more common wood like pine and such?
Pine and eucalyptus, mostly for finish carpentry (moldings), door frames, as well as plywood, MDF, particleboard, etc. Also logs for pulp and paper, as well as those wood pellets for home heating. This particular client does a lot of glued panels just like the one pictured, and makes pellets with their sawdust.
(A different client works with teak. Exotic hardwoods are big business but incredibly complicated...our oversight here may be a total joke but most foreign markets, particularly Europe, want things certified inside and out, which is really hard for exotic hardwoods since that involves seed-to-plank traceability, plantation practices, etc. These clients of mine are all FSC certified for the euc and pine they produce.)
Canada cuts down a lot of trees and exports it all over the world. Then we buy back the finished lumber and products.
It's entirely probable that the wood could have come from within a few hours drive from my house, depending on the kind of tree.
That said, in 2020, there was a massive switch in the manufacturing of wood products to focus on PPE (personal protection equipment) so there was a shortage of wood and wood products in North America. I bought eight-foot 2x4 for $2.14 in mid-2019, by early 2021, it was $18.99. Maybe wood from the Old World is now so much cheaper than local stuff that the US is doing the Canadian thing of importing finished products it while exporting the raw materials.
When they closed the mills and quit logging where I live they used to hire guys from here to go to New Zealand to show them how to farm timber and make good lumber out of 'em. They did it because the NZers planted our local pine trees there, and the local guys already new everything about those trees. Now they ship a lot of that lumber7000 miles back to California where it gets sold at Home Depot as "radiata pine". Yay environmentalism!