Can I use normal routine shampoo after 1 month FUE??

It is always a good idea to follow your doctor's directions after surgery. In general, after one month there should be no issue

Yes, after one month it is okay to go back to the normal haircare routine you had before your transplant procedure, including washing with your normal shampoo however often you like.

After one week, you can already use your routine shampoo, use directly the shower jet on your head, use water at a normal temperature. Actually, you can wash your hair as you used to before your surgery.

All doubts about the post operative period of a hair transplantation should be advised by the surgeon who performed the procedure first, but in general, after one month of FUE, the small holes after a FUE procedure are healed after 7 to 15 days. After this period, you can wash your hair with your normal shampoo. So, in my opinion, after one month, normal life. 

One month after hair transplantation,  you can resume your normal shampooing.  Still be gentle to the recipient area but you can touch the area and use your shampoo of choice. 

An FUE is treated just like a regular hair
transplant with regard to the recipient area, but the donor area has open
wounds which require daily washing with soap and water. 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 are 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 7-10 days with daily washing