It's from the Phaedrus, specifically section 248c (Socrates' discourse on the nature of the soul). I don't know whose translation was used in the film, but here's a translation (from the Greek) of the same lines: "Whatever soul has followed in the train of a god, and discerned something of truth, shall be kept from sorrow, and if she can do this always, she shall remain always free from hurt."

I've been looking too, with zero results. According to Dr. Feckenham, it's Plato - specifically, his commentary on the death of Socrates (as he told Jane at the beginning of the movie when she sight-translated the Greek she was reading).
I've searched online, and in also in sources such as BARLETT'S QUOTATIONS (after I first saw the movie in the late 80's).
The quote as spoken by Dr. Feckenham at the end of the movie and leading into the credits, is:
The soul takes flight to the world that is invisible.
And there arriving, she is sure of bliss,
And forever dwells in Paradise.
To me, it's a beautiful thought. I just wish I knew the source.
Jeff

As in "Phaedo to black"?
Seriously, I just went to this link and read the text, then searched it using "Find" after I couldn't see the quoted passage.
The Find function confirmed it isn't there. Not even the word "flight".

It's from Plato's
Phaedo
recounting the death of Socrates, who was
sentenced to drink hemlock after being condemned from corrupting the
young of Athens.
Here's a link to the entire text:
http://www.wsu.edu:8080/~wldciv/world_civ_reader/world_civ_reader_1/phaedo.html