It is so hard to do that IMO this should be fixed. First of all, it is impossible to drag harvested items directly to the fridge. What you can do is to drag them one by one from the family inventory and place them onto different surfaces. Imagine doing that with a stack of 99+ items 🙂. You cannot drag the whole stack. Event if you place the item on the surface, sometimes it becomes invisible (undo/redo in the builder fixes that though). Do not place items on the ground, because you cannot put them into the sim's inventory, you can only eat or plant them. So, say I place the item on the floor at each grid intersection and hope to place it to the sim's inventory. After you go to the live mode some items can be grabbed and some not. The ones which could be grabbed they could be placed to the inventory. With the rest you are unlucky... You have to put them back to the family inventory. Was that a lucky grid intersection which allowed me to grab the item from and other intersections are different? No. Even if you place another item at the same grid intersection you cannot grab it afterwards. So, basically, moving items is a matter of success.
Anyway, once you succeed to put items into sim's inventory, then you can move them to the fridge. But... well, if you succeed.