The hard part will be if you want to keep your projects separate.
By default, iFix puts all the project files in the /Dynamics folder, and the Backup & Restore Wizard will copy ALL of the files in the /PIC, /LOCAL, /PDB, etc folders.
Do as everyone said, and use the Backup & Restore Wizard to make a full backup of the customers system. Also copy the SCU file (.SCU extension) as a separate file.
What I would recommend you do is, first, open the old SCU file, record all the settings (name of node, database, PLC drivers, etc),
Create a new folder for the project on your PC.
Then create a new vanilla SCU file (using the System Configuration Utility), and change the project path (NOT the Base path). iFix will create default subdirectories and certain systems files.
Manually enter the data from the old SCU into your good SCU. (It may complain that the database doesn't exist - that's OK for now)
Save this SCU file in the /LOCAL folder of your new project folder.
Make this the default startup project (you'll be prompted).
Then, do a partial restore of the existing system. You'll want to check the box "Use Existing System" or words to that effect. Don't restore the old SCU.
When the driver file is restored, you may need to go into the driver, and set up the driver's configuration file (ex: iFIX.ABR) and path to be the default.
I just finished doing these steps, so the inforamtion is pretty fresh. I ran into some trouble, since security is turned ON for the customer's project, and I wanted it OFF. There were a few times when I got a contradictory set of error messages (Running SCU: "You don't have security rights to run this application"; Running Login: "Security is disabled on this node"). I wound up deleting the entire project folder AND the /Dynamics folder and re-installing (twice).
But it's working the way I want it. There are lots of gotcha's out there for you still, but I think that this might be the cleanest way to set things up for you.
Post again if you need more.