OK, in that case combining Raman and UV-Vis spectroscopy with MS (and eventually UPS) would be the best combination.
Each cage has characteristic absorptions which UV-Vis of a solution, e.g. in toluene, will show you. Then you can support that with Raman spectra which have also characteristic bands for each cage.
Final evidence for the cage mass is accessible via mass spectrometry, but since that's destructive, you should do that last. You can use an ESI ion source with TDAE or also an LDI source, but in that case keep the laser power at the lowest possible level; if you shoot a laser into anything that contains carbon with enough power, you will always observe graphitization and that leads to C60 formation.
If you have a surface deposit, photoelectron spectroscopy (particularly UPS) would also be a good option as that also provides you with a characteristic valence band fingerprint. XPS can also be used to verify the presence of sp2+x carbon, but that's not very specific in comparison with the other methods.
So, you have a mixed soot with all sorts of sp2 carbon? In that case follow the classical route for fullerene extraction (classical: toluene in a Soxhlet extractor, but you can check for newer options) and start from that solution.
Since you only need to verify the presence, I suppose, start with mass spectrometry in that case.
No, That is a new procedure in order to synthesize composite containing fullerene. In hypothesis, fullerene was doped with nitrogen or halogen I had the precursor-removing method. But determining and extract is a big problem. I think the product will have function group similar on surface =) similar dispersion.
In that case, low-power LDI or MALDI mass spectrometry would still be the first step, I guess.
PS: you asked the generic starter question again yesterday opening a new thread, https://www.researchgate.net/post/How_to_prove_the_presence_of_fullerenes_by_measurements. Do you really hope that you will get more meaningful answers by not providing relevant information?