Can I apply some moisturizer in the implanted area?

It is best to ask your surgeon about post operative care as each doctor has their unique regimen.  

Hello, Thank you for your question. Postoperative care is one of the important parts of the hair transplant. I always suggest to my patients to start using moisturizer 4 days after the procedure right before the washing. It always helps to the scabs falling off naturally and I can be sure that the scabs won't harm the receipt area. I expect my patients to have clean scalp with no crufts or scabs on 10-13 day post-op. In your case, since you are 12 days post-op, apply moisturizer, leave it for couple hours, then wash it properly with shampoo and do not hesitate gently massaging it with finger tips only. 

Within 3 days of surgery, you can resume full activities, heavy exercises if you wish. The recipient area requires daily washes as well to keep the recipient area free of crusts. I generally recommend the use of a sponge and supply my patient with a surgical sponge to fill with soapy water and press on the recipient area daily. By repeating this daily, all crusts can be washed off without any fear of losing grafts. IF any crust is present, use a Q tip and dip it into soapy water, and roll it on the crusts and that will lift them off without dislodging them, but never rub them, just roll the Q tip on the recipient crust. I like to see no evidence of any crusting in the recipient area and the crusts from the donor area gone in 3-4 days with daily washing. To get the crusting off, you need to leave the shampoo on your hair for 10 minutes and as the crust become water logged, then will come off with gentle finger action. Repeat this twice a day until it is all
gone. The use of a moisturizer is fine