Your freighters do not deliver the required goods at the destination? Here is (most likely) the solution.
Welcome to this quick solution (i hope). I had this problem myself and Google brought no answer.
To connect to an NPC outpost, you first need the Inter System Cargo Link landing platform (which requires Helium3 to function). I assume that you have packed the required goods into the outbound container (or connected a storage to it) and that there is enough Helium3 available.
You link your station to the NPC station via the terminal at the top of your Inter Sytem Cargo Link landing platform.
Problem and Solution
The freighter lands, takes the goods out of the outgoing container, flies off, and is never seen again? The quest is neither updated nor completed?
The quest marker still points to your landing platform? The solution is very simple: fly to the destination (where the goods are supposed to go), get on the NPC ship blocking the landing platform, park it somewhere else (or sell it as a punishment) and your worries are solved.