Transfer vJoy Configuration

There's a command-line utility under the vJoy folder (Usually C:\Program Files\vJoy\x64) called vJoyConfig.
It is used to detect the configuration of your setup and to change your setup.

Assuming you know which are your configured devices you extract a command-line per device as follows (Example relates to device #9):
vJoyConfig -t -c 1 9


You can also just ask for all 16 devices like this:
vJoyConfig -t -c 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
You will get a line per configured device. Here's what I got on my machine:
vJoyConfig 1 -f -a X Y Z Rx Ry -b 32 -p 1 -e all

vJoyConfig 9 -f -a X Y Z Rx Ry Rz Sl0 Sl1 -b 32

Just put these lines in a batch file and spread then around. There are more efficient ways if you are dealing with frequent changes.
Perhaps you should read about this utility here.