The J.G.I. mark is the mark of the silversmith who made it. Silversmiths all use their own personal markings; to identify exactly which silversmith or company made this piece, you would need to search through guidebooks to try and identify it. That's a rather esoteric task and is usually only done by serious antique collectors because there are literally thousands of silver plate markings that have been used over the centuries.

The EPNS stands for electroplated nickel silver (nickel with a thin silver finish).

The decoration on the outside is Art Deco style, which fits with the 1939 engraving date. Cigarette cases were popular gifts in the mid 20th Century and were commonly engraved and carried around as fashion accessories. Of course they also had a specific function as well, which was to keep cigarettes from being crushed while being carried in a pocket.

Antique/vintage cigarette cases are fairly common, so they are not usually worth a great deal of money unless they were made by somebody famous like Peter Carl Fabergé. There are numerous people who do collect them out of enjoyment, however.