Question

What do we do the leather material infected by fungus or mould ?

Answer 1

If it's me, throw away immediately. Leather is skin and something has “taken root” I would burn it.

Mould is a little different. Because leather is “"water proof” it can promote mould growth. You can wipe away with warm dilute soapy water. Worked for me. Look at where you are storing your leather as it seems it may be storage conditions. Also, try and keep your leather items separate from each other to minimise cross contamination.

I'm not a tanning expert but this seems logical to me without Googling it.