First, what vehicle are you using to move furniture? If it is an enclosed truck or trailer, first fog the trailer/truck interior the day. I’d wait for no less than 20 minutes before loading items.
I would create a contained area, outside truck to move furniture through, like a portable/temporary garage covered in plastic, enclosing both ends with plastic using a slit at each end to enter and exit. This can be set up outside or in a garage.
Start fogger for 20 minutes and then bring one piece of furniture into the containment with fog, keep fogger running at all times while cleaning/wiping down. Use a microfiber cloth to wipe all surfaces of the furniture including back, bottom, legs. Pull out each drawer and wipe especially bottom, back and sides. Reach into the drawer cavity and wipe out, including all dust. Repeat for each drawer, cavity and cabinet. The fogger is running the entire time to capture and destroy all the spores being released into the air.
Once that piece of furniture is complete, move it out of containment and pack. If you use a fogger at a high speed it may leave moisture on horizontal surfaces and should be wiped with clean microfiber cloth. You do not want to leave visual droplets on wood or leather furniture. The fogger should always be on low setting. Fog should be near invisible. We recommend fogger that will put out mist/fog at 3 microns droplet size otherwise droplets will be too heavy and fall straight down to ground when our goal is to have fog linger in air to attack and clean away airborne spores.
Other solid surface items like silverware, pots and pans can be lightly wiped or blow off dust in containment. Mold does not like these item to grow on, but will land and consume any dust on these hard surface items.
Leather furniture can be saved with a very careful process. We recommend HEPA vacuuming all surfaces. We recommend removing bottom thin lining to reach underneath side. Then take in fogged containment and particularly get fog on underneath side. Leave in fog 5-10 minute and remove out to pack. Be sure NO droplets remain on leather as it will mar leather. Another reason you need 3 micron fog. To be sure take dry, clean microfiber to leather surface once out of containment before packing.
This is all with MoldKlear Interior formula. Regarding clothes you can launder with regular load and add one cup MoldKlear to wash. Other items that cannot be easily laundered then can take in containment with fog, flutter clothes, goal to remove all dust mold likes to attach to. Leather purses, shoes, wipe with microfiber in contained area then pack.
Do not let furniture remain in an enclosed storage unit/trailer without good climate control.
Also, be sure and wear protective clothing, goggles and N-95 mask. Fog solution will not harm you but we are disturbing dust, particulate and spores you do not want to breath in or absorb into skin.
Make sure you test new living space so you are not trading problems.