There are two styles of aftermarket spin on oil filter adapters for 1956-67 Chevrolet V8 engines originally fitted with canister filters. The first style that you have is used in conjunction with the stock canister style bypass valve and uses a Chevrolet type spin on filter. This design relies on a felt washer to seal the adapter to the bypass valve. If the felt washer fails unfiltered oil will bypass the filter. Even worse pieces of the felt washer can come off and travel directly to the engine bearings. I never use this style of adapter.
The second design is the one I prefer. It uses a Ford style spin on filter. These filters have a built in bypass valve so there is no need to use the old canister bypass valve. To install this adapter you simply remove the old bypass valve, bolt the adapter directly to the block, and spin on a new filter. There is no felt washer to worry about and it uses a Ford-Chrysler style spin on oil filter which has the bypass valve built into the filter. This adapter is simple, safe, and uses the most common filter on the market.
Trans-Dapt 1024 adapter