You can issue a project box using circulate in much the same way you issue normal resources, however you can also do it directly from the project box record card itself.
Open the project box from within management and select the 'Issue' button.
A box will appear that shows the information of the box. Scan the borrower's barcode or press 'Find...' and locate them in the list, once selected their information will show in the bottom half of the box. When you have confirmed these details are correct, click 'Issue' to issue the box. You can then print the dispatch documents from the bottom of the window as a receipt.