You can update the Process of an XBert.
If you want these XBerts to appear under a different Process every time, you will need to update the Process against the XBert in XBert Automation.
From the work list or work board, open an XBert tile by clicking on the summary.
This will open a detailed tile on the right side of your screen.
From the Action Bar on the right side, the Tag icon will allow you to update the Process of an XBert.
Click Save afterwards.