. Trikoo would be the Finnish word for jersey (from the French "tricot") - so the company name does translate to Finnish Jersey. The company was founded in Tampere, which was THE centre of textile and shoe production in Finland for decades. They were strong in producing their own and also exported a lot to the USSR. Some of the factories were right in the city, as they were built to use the power of the river flowing through the city (I've been there and seen the old Finlayson factory building). Finlayson bought Suomen Trikoo up in 1983. Finlayson is still one of the major textile companies in Finland, and they do their own designs and all kinds of home textiles - not unlike Marimekko, but less well-known internationally and I think they export less. The name Suomen Trikoo was used until 1996. I found a few old ads and fashion shots for Suomen Trikoo in one of my books, ranging from the 30s to the 70s, but nothing showing anything like this sweater. It seems they produced all sorts of knits - fine jersey fabrics, chunky sweaters like yours and even hosiery.
... No, Finland was definitely not exporting to the US during WW2 - they were an ally of Germany, and from what I know, most of their exports after this first went to their neighbours. I have this huge book on the history of Finnish fashion photography here that would probably have a lot of interesting facts, but... it's all written in Finnish 
except for a short 4-page recap in English at the end. I just bought it because of the gorgeous pictures - my knowledge of Finnish is very basic.