There are multiple ways to move a sticky note from one folder to another in Notezilla for Windows.
One way to move the sticky note to a memoboard is using the top left button over a sticky note. Clicking on it will show a menu with 'Stick to memoboard' option. This will move the note to another memoboard. If you then wish to remove from desktop then use the Stick To Desktop option from the same menu.
Drag & drop is also possible.
The above article will tell how to duplicate a note. However, if you don't hold the Ctrl key then it will move the note instead of duplicating it.