Start the burglary missions and park infront of a barber shop. Enter said shop and walk into the red circle to take a seat. Press X to view a haircut and wait until the time expires. Once the mission has ended press triangle and the barber will "put" the mask back on you. Now you may leave the barber shop with the mask on your face. Note: You may not change your clothes or die/ get busted the mask will disappear.