Copy files from several folders to a single destination, with Copy All to One
Copy All To One is a freeware utility that will help you copy all the files from many folders to a single folder.
It supports extension select by filter, and the option to delete the source files after you copy them.
Another useful option is that you can automatically rename the files in the destination folder by adding numbering (this way you will avoid conflicts when two or more files have the same name.
* Check also Fetch The Target, a light and safe tool that will let you copy the targets of shortcuts, that is, the contents of the actual folders your shortcuts point to.