'transport box' is a correct and usable phrase in written English.
You can use it to refer to any sort of container or packaging used for transporting goods. For example, "The storage shelves were filled with transport boxes ready for delivery."
The animals were tranquilized in the transport box before the anesthetic induction.
About three weeks before Sunanda arrived, her transport box was delivered to her Dutch quarters.
For the lengthening procedure, the controller was placed on a table hooked into its transport box in an upright position (see Fig. 3).
The first of the three satellites, which was meant to go into space from Europe's Space port in French Guiana, was crushed during a flight from Japan after a blue tarpaulin covering its transport box blocked valves meant to equalize the internal air pressure as the cargo aircraft descended.
The transport box was kept closed for 1 min and then left opened for 3 min. The experimenter noted latency of emergence from the wooden box into the experimental box.
From the local chilling centre, milk is moved to the regional DDC chilling centres via road transport (Box 3.3).
Based on Clouzot's The Wages of Fear, it stars the wonderful Roy Scheider and Bruno Cremer as fugitives who've agreed to transport boxes of explosives through a South American jungle.
They are environmentally responsible: saving trees from being felled to produce paper, and fossil fuel from being burned to transport boxes of books.
The barn and the other dioramas will be transported to the Washington museum on a special truck, stowed inside custom-made transport boxes to minimize the effects of the truck's vibration, O'Connor said.
The samples of the transport boxes and workers' hands of the three farms were collected only at harvest.
I've used UberXL multiple times to transport boxes of books and stuff, a mattress, a chair — and I'm probably forgetting a few rides.
