Can I use sunscreen on my recipient area 2 month post FUE?

It is best to contact your doctor about post operative care and instructions since each doctor has a different regimen.  You should be able to use anything after two months.

Actually after two weeks of healing you should sun bock on the recipient area for at LEAST 3 months so the grafts do not get excessive sun and UV exposure. After the three months, everything will be ok including sun exposure. 

If you are to use sunscreen after an FUE or strip surgery, it should be started after 6 months following the transplant. Prior to this, your scalp is still in the process of healing and is very sensitive. Up to 6 months post-surgery, your scalp will be more vulnerable to the effects of the sun’s UV rays, which affect the surface of your scalp as well as the new grafts. If you are going to spend more than 30 minutes in the sun, you should protect your scalp - the best would be a hat for stronger protection.

No , using the sunscreen will not affect the growth of the implanted grafts. You may also use it for donor site 

In my practice, I recommend that patients use sunscreen on their skin and scalp after hair transplantation.  In general, it is safe after all the wounds have healed.  

YOU SHOULD USE SUNSCREEN IF YOU GO INTO THE SUN. IT SHOULD BE WELL APPLIED TO THE RECIPIENT AREA. ALTERNATIVELY, YOU CAN USE A HAT