Black mould inside a stud partion due to leaky pluming

[mikea]

I have found small area of black powdery mould on the inner paper surface of the plasterboard on a stud partition caused by a leaky recessed shower mixer.
The worst extent of the mould is along the contact between the pasterboard and the vertical wooden battens of the stud, persumably because this is where the moisture in the paper was least able to dry out. Having fixed the cause of the damp and removed most of the mouldy board is it necessary to proceed and remove the mouldy board as far as the extent of the mould and then treat the exposed wood? Will the mould continue to spread in the abscence of further moisture? I am reluctant to do more than necessary since removing the tiles is difficult - hard epoxy grout and no spare tiles available in case of breakage.