How can I convert .STL file to .OFF to use in CGAL?
If you can handle a single intermediate step, you may find that OpenSCAD will perform as required. As a test, I created a cube 10 x 20 x 5 within OpenSCAD.  I kept the model simple, hoping the code generated would be short.

The results:

OFF


8 12 0

0 0 5

10 0 5

10 20 5

0 20 0

0 0 0

10 0 0

10 20 0

0 20 5

3  4 5 1

3  0 4 1

3  0 7 4

3  4 7 3

3  0 1 2

3  7 0 2

3  3 6 4

3  4 6 5

3  5 6 2

3  1 5 2

3  7 2 3

3  3 2 6

In your example, it would be necessary to use the import_stl feature of OpenSCAD, then render the model. Once rendered, use File, Export, Export as OFF to create the file you need. 

I cannot provide certainty of the exported code, however, as I am not familiar with the format you seek.

Openscad