Surface export not matching MRI space

Thank you for your quick answer.

The first thing I tried in this project was to use the cs_convert function on the vertices and faces of the pial found in the anatomy folder in the brainstorm database. However, it caused issues with stlwrite.m.
data = load('pial.mat')
Fk = data.faces;
Vk = data.vertices;
sMRI = load('subjectimage.mat')

[Fk, Transf] = cs_convert(sMri, 'scs', 'mri', Fk);
[Vk, Transf] = cs_convert(sMri, 'scs', 'mri', Vk);
stlwrite('test_HEJ_suj12.stl',struct('faces',Fk,'vertices',Vk));
Index in position 2 is invalid. Array indices must be positive integers or logical
values.
Error in stlwrite (line 76)
facets = reshape(facets(:,faces'), 3, 3, );

I supposed that te error was due to the conversion of the surfaces so I tried to apply the .stl to only the vertices to which I applied the cs_convert(scs to mri (i suppose this the correct format)). And As you can see the result is not great to say the least.

Then I tried to export directly the file pial (in brainstom: anatomy>subject>pial>right clic>file>export file>.gii or .fs) thinking that they would be converted back to the original MRI system but as you can see it did not work (1st post).

Is there any other export method that would convert the pial back to the original MRI system ? Or if you have the information of what is the conversion matrix of the exported pial file (from the previous paragraph) ?