While West Germany's NATO partner Britain is at war with Argentina, construction continues in a shipyard at the town of Emden on a submarine for Argentina, part of a larger arms package that has brought new attention to Bonn's role as an arms exporter.

A ban on West German arms deliveries to Argentina has been in force since the Falklands conflict began. But construction on orders already placed continues, and if Argentina's small submarine force should go into action, it will include two German-built U-boats--the Salta and the San Luis--commissioned in 1974.

West Germany ranks as Argentina's main arms supplier in Europe. The battle in the South Atlantic comes as the Bonn government has issued a set of new guidelines on arms exports allowing it to be a bit more openhanded about weapons sales.

The new rules, approved by the Cabinet last week, replace an 11-year-old self-imposed prohibition against arms sales to "areas of tension." The restrictiveness of the previous guidelines had reflected uncomfortable memories of past German militarism and sensitivity to what the world would tolerate even from a reformed West Germany.

But West German arms dealers, looking to cut manufacturing costs by adding production for export, still managed to build up this country's position as a weapons exporter to rank fifth in the world behind the United States, the Soviet Union, France and Britain.

In 1980, West German arms sales reached about $900 million. While still less than 1 percent of total exports, the value of weapons exports has risen in recent years, and some in the industry see themselves at the "takeoff" stage of development.

As for sales to Argentina, which was not considered an area of tension before April, West Germany is not alone in arming the military government there. The French supplied Mirage fighters, helicopters, radar-guided missiles and corvettes. The British themselves provided antisubmarine helicopters, destroyers and missiles.

But West Germany's contribution is noticeable. Thyssen Nordseewerke in Kiel, the builder of the Argentine submarines, also has contracts to provide plans and materials for five more ships to be built in Argentina.

Another Thyssen subsidiary, Blohm and Voss in Hamburg, is constructing four frigates for Argentina and supplying plans and materials for six corvettes. The Tam combat tank now in production in Argentina was developed by another Thyssen firm.

In aeronautics, too, there are West German connections to Argentina. Dornier International is helping Buenos Aires develop the IA63 jet, and technology from Messerschmitt-Boelkow-Blohm was used in the early phase of development of the French-made Exocet missile, responsible for sinking the destroyer HMS Sheffield and the cargo ship Atlantic Conveyer off the Falklands.

Germany's military relations with Argentina have a long tradition. In the 1800s, Argentina already was building Krupp-model cannons. When Argentina's first military academy opened in 1900, the director and four of 10 instructors were German officers.

West German arms sales became a heated domestic political issue early last year, when word emerged that the government quietly was considering supplying two submarines, originally intended for Iran under the shah, to the military government of Chile. The topic broke onto the front pages again when it became known that Saudi Arabia had indicated an interest in buying the advanced Leopard 2 tank.

Both potential sales upset the left wing of Chancellor Helmut Schmidt's Social Democratic Party. The Saudi deal in particular bothered many West Germans sensitive to providing weapons that could one day be used against Israel.

While Schmidt would have preferred to sell the tanks to the Saudis to cement an important Saudi-West German economic relationship and to contribute to Persian Gulf security, resistance from his party and from the Free Democratic Party in the Bonn coalition prompted a formal reassessment of the government's whole arms-export policy. This resulted in the new guidelines.

The revised rules represent a victory for Schmidt and those intent on preserving thousands of shipbuilding and aviation jobs.

The flat ban on exports to areas of tension is gone. West German arms sales to countries outside the North Atlantic Treaty Organization can be justified in the future by "special political considerations" or, in individual instances, when Bonn's "vital interests" are involved. Such interests are loosely defined as "foreign and security policy taking into account alliance interests."

Explaining the new guidelines, a government spokesman stressed last week that they would not be used to ease approval for export deals. Bonn, he said, would continue to observe a "strict and restrictive interpretation" of the rules on sales outside NATO.