Earning money on Shabbat for permitted behavior?

Question

If somebody gets a Heter from a rabbi or posek to do something on Shabbat that is normally forbidden for pikuach nefesh (such as being a police officer, firefighter, etc.) are they allowed to earn money from what they do? There is a rabbinic prohibition against money handling on Shabbat, but this doesn’t generally apply to cases where they are being paid as part of a larger salary beyond what they do on Shabbat (such as a Cantor/rabbi who gets paid for Shabbat services as part of a larger payment for their duties they also do during the weekday). Does this reasoning also apply to work that involves melacha but is still allowed nonetheless for reasons mentioned? Sources appreciated