Det bästa stället att spara veden är nog på banken...
Sälj veden till någon som behöver den. Sälj den billigt så du blir av med den. Köp sedan ny ved nästa år. Du får nog inte lika mycket ved, men i gengäld är den frisk och inte möglig. Gräsmattan kommer att vara prydlig.
Trots att du får mindre ved nästa år kommer du troligen att få minst lika mycket värme när du eldar den, och du slipper bli sjuk av möglet.
The best place to store the firewood might be at the bank...
Sell the firewood to someone that needs it. Sell it cheap so you get rid of it. Then buy new firewood next year. You may not get as much wood, but on the other hand it will be fresh and without mold. Also your lawn will be tidy.
Despite that you get less wood next year, you will likely get at least as much heat when you burn it, and you avoid getting ill from the mold.
Otherwise the best way to store it is perhaps very wet and cool, water it daily and keep it in the shade. That is how large sawmills store excessive lumber after storms.
You could also remove the bark and attempt to dry the logs without cutting them, but I don't think that is worth it.