using other freesurfer surface to project maps

Hi Alfonso,
I would like to substitute the \surf folder in the CONN installation with the outputs of Freesurfer (FS) on my specific data.
I have a set of ROIs masked using a specific mask in a specific volume. I used this volume to generate the Freesurfer /surf folder.
However, the FS output files are the same in CONN's /surf folder. For example, lh.pial.surf in CONN is merely lh.pial in the FS output. Also, cortex and mid surfaces are not present and the registration is not symmetric as in CONN, i.e., right and left surfaces do not have the same number of trianges. Thus, even if I trick CONN by renaming some files and reusing them for other types of surfaces I still get an error due to this difference between hemispheres. 

I wonder how this CONN's \surf was created and how I can adapt my data to its format.

I am attaching my output

Thank you!