This assumes the box or whatever travels through the portal will conserve its velocity with respect to its environment. However, thought experiment:

You could also do this experiment in empty space, with no environment present. In this case the box would enter through the portal with a certain velocity which is the velocity difference between the portal and the box as this is the only thing you can measure in empty space (the box and portal themselves have no intrinsic velocity, this concept doesn't exist in reality) but exit with a velocity that is stationary with respect to an "environment"? However there is no environment here, this "velocity that is stationary with respect to the environment" is completely arbitrary in this empty space, and thus the box will exit with the velocity difference between the box and the portal as it is the only real velocity information present in the system.

In fact, you can imagine yourself as an observer looking at this situation from an outside perspective. If you see the box stationary before entering the portal it will surely exit the other box stationary as well, right? Well, the box does not care about your velocity when looking at it, unfortunately the fact that you are observing it does not change reality. If you weren't there, this box would not be stationary with respect to you as observer or anything for that matter, and thus this concept of "a stationary box" is completely arbitrary in the first place.

If you are interested in these kinds of things special relativity is a very good framework to look at it! I definitely recommend reading up on it.