For a female to male surgery, can doctors construct a penis?

Yes Drs. can. Surgery is very complex & can be performed by a number of different techniques. Probably most successful is graft from the forearm. Other techniques include graft formed of chest or leg, or flaps from abdominal wall. Skin flaps remain attached to their original blood supply as first of 2-stage procedure & separated from original "donor" site as 2nd. stage.