You have to remember that Portugal was Britain's oldest ally, dating from even before the Spanish Armada in 1588. Portugal declared war on Germany in 1914, coming in simply because Britain was their old ally.
In the Great War, the Portuguese were using their Vergueiro rifle, which was a 6.5x58. Trouble was that both rifle and ammunition were made in Germany and those guys just have no sense of ha-ha at all. Just declare war on 'em and they won't sell you any more bullets!
So Portugal ended the Great War just about completely equipped with British materiel: uniforms, helmets, SMLEs, Lewises, Vickers guns et cetera.
That nice Mister Hitler wanted to obviate such a situation coming to pass again, and he had his buddy Franco to threaten the Portuguese into the bargain, Spain never really having forgiven Portugal for breaking away, back in the time of Henry the Navigator and cohorts. Portugal's government at that time was just a little bit right-wing and the Brits wanted to keep them happy. So did the Germans. So the Germans came up with a really good deal on a whole bunch of real nice Kar 98ks, MG-13s and other suchlike toys.
Rifles shipped to Portugal generally were fully marked as German equipment, with the addition of a large, prominent eagle-and-swastika on the butt. They also were treated to full Portuguese markings. Portugal adopted the 7.9x57JsS round as the M937 and kept it in reserve until the 1980s, when the rifles, MGs and ammo finally were sold off as surplus.
Rifles I have seen were all manufactured by Mauser and seem to have been finished to commercial standards. They were really lovely. I couldn't afford one at the time they came out and still can't.... but they are a beautiful piece of equipment and a real chunk of history.... almost a birthday present from Uncle Adolf to his Portuguese pals.
Portugal stayed neutral during the Second War, although its sympathies were with the Allies.
Guess the kind words and almost-free toys ..... and the threats from Franco..... worked. In 1942/44, Lisbon was the spy capital of the world.
But they are just so beautiful.