Sorry for the response delay.
No, there is no easy solution to convert between surface and volume atlases.
But, there are already available in FreeSurfer. After processing your MRI with FreeSurfer, you have access to the Desikan-Killiany (aparc+aseg.mgz) and Destrieux (aparc.a2009s+aseg.mgz) atlases as volumes:
https://surfer.nmr.mgh.harvard.edu/fswiki/FsTutorial/AnatomicalROI