Answer:
Yes, we can classify the organisms in the kingdom fungi because the organisms show all the characteristics which are present in fungi. These characteristics are spore formation, presence of cell wall and structure of mycelium. These three structures are enough evidence to classify the organisms in the kingdom fungi.
One more thing, we have to check the cell wall composition. If the cell wall is made of chitin so it is fungi but the cell wall is made of cellulose so it plant like fungi which is a protist not fungi.