Your FAC mod slot is permission to acquire and use according to the conditions on the cert. You can do as you suggest and declare the mod you already possess for addition to your cert. It would have to be sold on from you as an 'on ticket' mod. One issue with doing this is that you are generally not supposed to write anything other than your own signature on your cert, although I have read on forums of holders doing this under your circumstances. You'd be best asking your FEO how they would want you to go about doing this.
This also assumes that the mod is the right calibre for your FAC rated air rifle.