Oadi, you can store your Fusarium spp isolates in sterile soil for a long period by inoculating sterile soil in vials with mycelia and conidia. Alternatively, you can store the isolates on sterile filter paper in sealed envelopes at 4oC. For the latter, you grow the isolates in water agar to which strips of sterile filter paper were added. After a few days, you harvest the papers into sterile paper envelopes and dry over silica in a dessicator prior to cold storage.
I have preserved spores of Fusarium spp, in sterile distilled water successfully, up to 5 months before passing them to other media, it may be an idea when you want to start testing
Cultivate Fusarium spp. on PDA cotaining plates for 5-7 days, then cut small plugs, transfer them into cryovials and cover them with of sterile glycerol (50% [v/v]). Store at -80°. With every plug you can start then a new culture.
Grow Fusarium spp. on potato dextrose broth, filter the mycelial mat with whatman filter paper and then lyophilize the mycelia with lyophilizer at -40 centrigrade. and store the tubes in deep freeze.
Hi grow Fusarium on Whatsmans filter paper #3, when fully colonized pull of the paper and dry in sterile petri-dishes. Store half in a freezer and the other half cut with sterilized scissors into small pieces (0.5x0.5cm) and place in a sterilize glass vial. You can store this in a fridge at 4 to 6C.
Already your question is answered with simple and best ones. There are several methods. But, select the one which suits your infrastructure. ATCC follows best methods which keep the cultures keeping their original characters.