Stick a computer on the moon, put a mirror of the Web on it, and let it serve queries over shortwave radio. Then all a fallen civilisation has to do is re-discover radio, to get access to the world's knowledge.
And reverse engineer TCP/IP, HTTP, unicode, etc.? Maybe we should come up with a simpler one-way protocol and just broadcast the whole thing continuously, on loop.
How would you power it? How would you protect it from the cycles of heating and cooling every lunar day? How would you protect the circuits from long-term damage, like electromigration?