After configure your watermark in Add Watermark window, you can click on Save Settings to save watermark as template, and you will find it in the dropdown list for Saved Settings for quick access.
Each saved watermark will be saved as an xml file in the below folder.
C:\Users\XXX\AppData\Roaming\Foxit Software\Foxit PDF Editor\PageFormat.
The watermark can be created by inputting text (Text source)or the existing file(File source), to move these two kinds of watermarks, you can refer to the below methods.
If your watermark is created by Source "Text", you can just save the xml file into the same folder for the current Foxit.
But if it is created by Source "File", beside importing the xml file, please ensure that the original source file should be saved in the same location as the previous. For example, when you create watermark with a file named A.jpg in D:\Documents, on the new reinstallation of Foxit, A.jpg should be saved in D:\Documents, then the watermark will be imported successfully by xml file.