I probably read this book as a mass market paperback, late 1980s.
A friendly pair of aliens from another universe crashes on the moon; we take it in on our moonbase. It is pursued by a violent, conquering race of aliens. These latter attack our moonbase one at a time, in increasing rank: first a trooper, then a sergeant, then a captain, finally a general (or ambassador). The aliens are universe hoppers, from another universe (not a "parallel universe" as in sideways-in-time stories, just a separate spacetime), and this was the first time encountering our universe. The aliens do increasing amounts of destruction to the moonbase yet we destroy each one -- until the ambassador comes and we make peace, somehow or other.
I believe the element fluorine had something to do with this, as a weapon of some kind that we used against the conquerors. (This is not Alien from the Stars which also touches on fluorine).
I also remember a scene where the friendly alien was complaining about being trapped in its suit.
Holographic recordings of corridors in the moonbase were used by the humans reconstructing what happened after an attack.
The author is NOT Jeffery Carver, or Robert Drake, or R. L. Fanthorpe.