Now projects are strongly connected to their locations on the computer. Even if you export project, it's connected to files on this very machine.
Add a new action "Export project with data..." int he "File" menu between "Export project..." and "Close project". When you click on this button, the dialog "Save project to" appears. You choose the directory and the name without any resolution (because it's a folder name". After you choose, the folder creates in the chosen directory, the project file and the all data saves in this directory. If you move this folder to another computer and open the project from this folder, UGENE automatically finds the all inner files.