The “F” word has been around for a long time, but it was previously known as an acronym: For Unlawful Carnal Knowledge and was painted on the stockades of people who committed adultery.
Its use as a word wasn’t really widespread until the 20th century and was generally meant to mean “sex.”
The F word dates back to the Middle Ages at least and is probably much older (the German, Norwegian and Dutch languages that are related to or have had influence on the English Language in Anglo-Saxon times have similar words meaning the same thing as the ‘F’ Word).
It could not have survived until the 1890s unless it was in common usage outside of polite society. Back in the 1860s, it would probably have been seen as so far beyond the pale that its use would not have been typically recorded in documentary evidence, but it must have been used, or else it would have been lost. Not everyone was a lady or a gentleman back then...
I don't know where you got your information, but the F word meaning sexual intercourse has been in the English common language for at least 1000 years. The word is used in Chaucer's “The Canterbury Tales” (The Miller's Tale, precisely), from the 1100s and it was an ancient word then.
Perhaps what gets some people confused is that prior to the 20th century, the word was ONLY used to mean sexual intercourse; not as a utterance closer in meaning to “damn,” or a noun meaning a cheap sex partner, etc.