He wrote in his last email:

THEN i realized something was wrong : bluetooth service support (in services.msc)

I searched a lot, then i applied this solution:

"Go to START icon and type in services.msc and select services.

The dialog box that opens has a long list of stuff but look for BLUETOOTH SUPPORT SERVICE. Double click to open. Make sure it is AUTOMATIC (it was for me). Go to the LOG tab. Choose THIS ACCOUNT and type in LOCAL SERVICE. A list of password (a 15-dot string) would appear. Delete all the password in the PASSWORD and under CONFIRM. Choose Okay.

(for me , it was this account but with a password of 2 dot string ?)

It will ask you to restart the service. Once restarted, turn on your bluetooth adaptor again. Put your mouse in pairing mode and add the mouse."

It WORKS PERFECTLY. I was really surprised !