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Apex Interstellar Transport
Dock to a starport, disembark from your ship, walk into the concourse. From the express elevators/lifts you already see a sign "Apex Interstellar Transport", walk towards that.
When you reach the counter, use E key to interact with the counter guy or girl. In my example case it was a guy.
First he gives you options for "I want to book a local shuttle." and "I'd like to book a long range shuttle.".
On local shuttle you just super cruise in the same system, you can be dropped off to a planet or other starport.
On long range shuttle you get galaxy map to select a drop-off point. I tried to select drop-off point in a system 675.23LY away but interface told me "Cannot book shuttle out of range" aww maan 
I saw the galaxy map having route plotted in blue type color, followed the route back to the origin and it was really unfortunate to discover that longest this shuttle will take you in my example case was 88.10LY away. This shuttle route had super cruise fee 100 credits and hyper space fee 43.9k credits.
Guess the price is OK for less than 100LY but dunno man I really hoped this apex interstellar transport would take you much further faster (not that I know even how fast it is, will it be a real legitimate AI ship that flies you there, no idea).
Its unfortunate that if you must travel quickly to your ship that is hundreds of light years away, there is no other option than to perhaps buy a throw away hauler or something and use that to taxi yourself there