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That is a good question, and one folks have asked us by email a few times. Thanks for prompting us to answer it here on History Hub!
Tough an old-fashioned “s” can sometimes look like an “f”, you should transcribe it as “s”. It’s known as a long S (and by a few other names): https://en.wikipedia.org/wiki/Long_s. Since we are transcribing for searchability, we want to replicate the words as they were written, rather than how they look.