Menzies, the Conservative Party member for Fylde in Lancashire, is the head of the cross-party British-Argentine parliamentary group. He is also a member of the Finance and International Development committees.
Menzies' role expands the growing ties between London and Buenos Aires, which were on full display during Prime Minister May's visit to the country for the G20 Leader Summit last weekend.
May's was the first visit by a sitting UK prime minister since the end of the 1982 South Atlantic War between the two countries.
The trade balance between the United Kingdom and Argentina sits at £1.5 billion (US$1.94 billion), according to data supplied by the British Embassy in Argentina. The UK imports Argentine goods and services to a total of £900 billion while exporting £600 billion.
Among British exports to Argentina are pharmaceuticals, energy, chemical material, metals, laboratory equipment, drinks, vehicles and plastic products. Meanwhile, Argentina exports predominately grain, primary commodities, animal feed and wine.