the serial monitor says 
PS/2-mouse to MSX-mouse converter for Arduino version 1.1 --------------------------------------------------------- Made By: NYYRIKKI 2014 Initializing PS/2 mouse...
So now I have to do the wires
YES YES !! I did the wires and connected the mouse to my MSX. Wow!
It works !!! in Symbos I can move the mouse !! Cool to have an optic mouse now. In the end I used a old USB mouse.
Only the scroll Wheel is not working .. hmmm .. it was all about the scroll wheel not .. any idea ? maybe I have to ask prodatron if I have to correct version.
I cannot say. If I connect the Nano to the PC it seems the mouse don't get power. (The optical led is not burning) so the Nano does nothing. (only saying Initializing PS/2 mouse... in the monitor) .. But If I connect the Nano to the MSX the Mouse gets power (the optical led is burning!) but when the nano is connected to the MSX I cannot connect the nano to the PC also ? (Because of power blowups ?) You warned me about that 
In the meantime I will read the manual sorry for that ..
Are you referring to this:
Usage:
Press reset = Mouse mode
Press reset & hold right mousebutton down = Joystick emulation
Press reset & hold left mousebutton down = Mouse + Joystick emulation *
If you have mouse with a scrolling wheel (optional) you can use the
wheel to adjust speed of mouse and/or sensitivity of joystick.
If status LED does NOT blink check your PS2-mouse connection and press reset.
I cannot say. If I connect the Nano to the PC it seems the mouse don't get power. (The optical led is not burning) so the Nano does nothing. (only saying Initializing PS/2 mouse... in the monitor) .. But If I connect the Nano to the MSX the Mouse gets power (the optical led is burning!) but when the nano is connected to the MSX I cannot connect the nano to the PC also ? (Because of power blowups ?) You warned me about that
Hmm... That is a bit weird... My mouse starts up correctly even when I have only USB-cable connected... Maybe your mouse requires a bit more power or something like that...
ahh : RTFM .. I hope my timing is perfect as I can't use the monitor if it's not connected to the PC.. Let's try...
Example, how to setup Symbos compatible mouse wheel support as default mouse mode:
- Hold down button 2
- Power on MSX
- wait until MSX-logo has disappeared.
- lift up button 2
- click button 1 once
- hold down button 1
- hold down button 2
- release both mouse buttons
Yes, I agree that setting up default mode requires a bit finger acrobatics, but luckily it is rarely needed to change the default mode. As first time power up mode I selected compatibility mode that means scroll wheel is used only to adjust sensitivity. Even when you can't see the monitor, you can see the currently selected mode by calculating blinks of the Arduino embedded status led during boot (If you have not yet boxed your adapter)