Please use: s001_tess_cortex.mat.
If your file is really called s001_tess_cortex.mat, then you manipulated the contents of the database manually, you may have damaged something on the way. The file names generated by Brainstorm are all starting with the file type (eg. 'tess_...mat`). Please do not manipulate the files outside of the Brainstorm database explorer if you are not 100% sure of what you are doing. Or if you are decided to modify the file structures, please respect all the conventions.
Starting by reading the Scripting tutorial might help you:
https://neuroimage.usc.edu/brainstorm/Tutorials/Scripting
The cortical file associated with these sources no longer exists.
When copying the head model with the GUI, the field SurfaceFile should be emptied, exactly to avoid this error you reported.
Example, based on the EEG/Epilepsy tutorial:
I duplicated the subject, then deleted the head models in the copied subject, and finally copy the OpenMEEG headmodel into the new subject. I right-click > File > View file contents on the original file and the copy. You can see that the copied file as no SurfaceFile reference, and therefore no possibility of generating the error you reported.
Your problem resides somewhere else than in the copy of the head model.
If you can't figure out the problem, please reload your protocol, then make sure the error is still there, and post screen captures of your database explorer showing all the files involved in the computation: cortex file (with the mouse over the file to show the tooltip with the file name), channel file, head model before copy, head model after copy. Include screen captures of the file contents as well.