Hello from JustAnswer.
I appreciate that you would like to help with the development of a vaccine, but if you were to send the sputum to a lab, it would no longer be able to be used for this purpose. To the extent that they could use sputum for this purpose, it would need to be a fresh specimen, rather than one that has been shipped.
They actually primarily use viruses that are grown in viral cultures to be able to develop vaccines, rather than directly from sputum. And once they have a good culture of any particular virus, there is no real benefit of collection of specimens from additional patients.
So, it would be fine for you to discard this sputum specimen.
If I can provide any additional information, please let me know.
Please let me know if I can provide any further assistance.