Not, the moon is a spacecraft. Found by two astronauts the craft and sentient AI spawn space adventures and somewhere along the line an academy is founded on the moon. Please help me remember this series
This sounds like the Slaver Wars series by Raymond Weil. The elements described by the OP, 2 astronauts, spacecraft with female AI and the academy on the moon are all present in the series although it has been a while since I've read any of them. The first book in the series is Moon Wreck which covers the astronauts and spacecraft AI discovery. A later book is called Moon Academy which is self explanatory.