Transmission line fittings

[Tonner]

I have a '72 C20 with a TH350 transmission. I bought it in pieces, so I never saw the transmission cooler lines connected. Both ends of both lines have flared ends and fittings. One of the flare fittings on the transmission end is screwed into a separate brass adapter with the same size threads and a flat end. Of the four ends, it's the only one and there are none in the bolt bags I received with the truck. Is the adapter supposed to be there? Should both lines have one? Should both lines have two? What is the adapter called and where do I get more? I tried threading them all in as-is, but the non-adapter line leaks from the transmission end. All appeared to tighten just fine.