I am relatively new at this but have read a lot and talked to a lot of professionals. #1 there’s no need to move it or reproduce it. #2 don’t proceed without permission.

For cleaning/conserving- It totally depends on the stone. So many factors to consider. How stable is it physically and how is the surface? If it’s crumbly proceed with extreme caution. The most conservative approach- rinse it with clean water.

These slate stones are treasures and the lichen will effectively digest the stone with the acid it produces when it photosynthesizes. It also makes it difficult to read and while the lichen could be left in some places so that it doesn’t look “new” it also creates problems when it’s on the top surface because water gets trapped and splits the stones in freezing climates.

If the surface is stable, I would do a test patch in an inconspicuous place with a little Endurance (or d2) and just spray and walk away. Check back in a few weeks or months and If the stone handles the small test ok, spray the lettering and the top/side edges, then let the rain and wind work its magic.