CAN I PUT THE EXHAUST TUBE INTO STORAGE CLOSET INSTEAD OF PUTTING IT IN A DOOR GOING TO THE OUTSIDE?

I think you are asking about a portable air conditioner, not a de-humidifier. With that assumed, the answer is, NO - that is not a good idea. The exhaust tube is for getting rid of the heat that you have pulled from the room you are cooling, plus the extra heat that the device itself creates. This is a considerable amount of heat, which will quickly heat up the closet and leak back into the room you are trying to cool. If the closet it tightly sealed, the unit will not be able to push the air through the tube, and the unit itself will overheat. The result will be that you will be buying electricity to actually RAISE the temperature of the room you are trying to cool.