I won't proclaim to be an expert, but here's what I would do.
Make some cross cuts at what you perceive to be the most damaged areas.
Now make a few other cross cuts at what appears to be the least damaged
areas. Using an awl poke and dig top, sides and cut side (probably end
grain). Also test a few random areas at what appears to be non-damaged
surfaces that have been at least 18" above the floor and as far away as
possible from walls, ceiling, windows and doors. Good stock may be just
slightly softer at the fresh cut end grain. Well dried stock should not
have that much deviation in softness. Try the same test using a known
well dried piece of lumber you think is the same species. This is a
general dry rot test. If it's rotten it will be soft and easy to push the
awl deep into the wood and will crumble if scraped.
Within the cuts look for color variations, mold, fungus, water stains,
etc.. Try planing or sanding down a section that is discolored and see
how deep the stain continues.
Good wood especially old growth mahogany can be exposed to moisture for
many years without failing. Look at some old boats.
Cut off the worst sections and discard or try and plane down to a good
surface. Brush off any fungus, wipe down with an anti-fungal (only if you
really think you need it, they often will discolor the wood). Sticker and
stack as if it was freshly milled wet wood. Start of stack should be at
least 18" above ground. There should be air gaps between sides of each
board and stickers between each layer. The entire stack should have
preferably 18" of clear space around all sides, top and bottom. If
possible have a fan to circulate the air.
I hauled away a junk mahogany and teak boat and recovered well over 70%
of the wood. Essentially free wood except of course for quite a bit of
labor involved in reclamation. I still have a few pieces and I feel it is
of higher quality than many of the young new-growth mahoganies being sold
today. The teak was near perfect after re-surfacing. Plus it can be a
sales point. Many of the yuppies prefer to purchase items made from
recovered product like fences, barns, broken furniture, etc..
I have the luxury of not having to warehouse purchased exotics with
recovered wood. I would keep a careful check on the drying condition and
possible contamination if I needed to mix expensive stock with recovered
stock. I have not yet had a problem with cross contamination from trees
recovered from the ground or other mold and stain issues. I have however
rejected wood/trees that appeared too rotten to recover enough to be cost
effective. I am more concerned about possible termite and beetle transfer
in my sheds, although I haven't had that problem yet.
The wood in your pictures doesn't appear to be that damaged but I would
go on feel (above awl test, and cut density) rather than sight.