I recently had a water tank explode and have been doing a lot of research on this.
Many will tell you to just mix laundry bleach 10:1 with some dish soap and apply it to the wood, let it dry then paint over it. This would be fine for a non porous surface, and if this area isn't likely to ever see moisture again it may be sufficient, however, in porous surfaces like wood mold grows roots into the wood that cannot be killed by bleach (bleach leaves it's chloride killing component at the surface).
Because of this, non-toxic household acids like vinegar, bases like borax, or hydrogen peroxide is preferred over bleach for porous surfaces such as wood. Adding a surfactant such as dish-soap should help with the penatrance. However, unless this solution penetrate deeper than the roots grown by the mold you won't be able to fully kill it, but it's also likely that no other moisture will penetrate that deep to reactivate it either.
*Beware *
You shouldn't mix any of the following cleaning solutions:
- Bleach + Vinegar (or ammonia) = chlorine gas (and ammonia isn't useful on mold anyway)
- Hydrogen Peroxide + Vinegar = Peracetic acid a strong irritant
Also not that contrary to what some websites might claim the following is counter productive(however, one followed by the other should be useful):
- Vinegar + baking soda: Mixing this acid and base together causes them
to neutralize each other diminishing the effectiveness of the
cleaning solution.
- Vinegar + Borax: Mixing this acid and base causes
them to neutralize each other diminishing the effectiveness of the
cleaning solution.
- Vinegar + Castle soap: Mixing this acid and base causes
them to neutralize each other diminishing the effectiveness of the
cleaning solution.