This is the place to post questions and discussions on usage and style. The members of the Wordwizard Clubhouse will also often be able to help you to formulate that difficult letter.
In a broad sense, it's a planter box. More specifically, I'd go with window box or window planter box.
Plant trough and garden trough.
You might like to compare with images of jardinière.
I'm puzzled therefore I think.
Thank you guys so much.