Birth Record in GRO

When a foreign born person is registered/naturalised as a British National, is his/her birth (details) "automatically" transferred to and kept by the General Register Office (GRO) in UK. If not, what can be done to make the GRO to keep the birth record as a British National.

That is not possible. The person was born outside the UK. Their birth certificate issued in the country of birth records that event.