Portal is one of my favorite games, and it's easy to see how you took inspiration. The style, the narrative (although I couldn't hear most of it, some subtitles would have helped) and the puzzle all scream Portal to me, which, I'd argue, it's a very good thing, since I enjoyed them, especially the last puzzle, since it was way more complex than the others, and I found it very fun.
I had some troubles in the beginning understanding how to use the DPTDD (maybe you can find a more endearing name), so maybe a little tutorial or even a small text would have helped.
And even though i really liked the main mechanic, i fell like there is the possibility that you may get stuck in a puzzle, since sometimes the physics on the boxes can act a little weird.
The thing that annoyed me the most is of "delicate" the boxes are: as soon as you graze any surface, you let them go. The problem is that it happens way to frequently, because when I pick them up I usually am looking down, making them hit the ground and immediately letting them go.
Also, some smaller nitpicks, in the last level I think you should be able to be carried by the "big rotating bridge" at the beginning, and the ending needs some clarification, since the game just closing left me a bit confused