Fi is the seventeenth letter of the Samaritan alphabet and carries the numeral value eighty. It stands where Hebrew has pe, and its name records the reading of the letter in the Samaritan tradition, where it is sounded f rather than p. That is why the standard character name for it is Fi.
The Tiberian reading of Hebrew gives this letter two pronunciations, a stop and a fricative, distributed by position and marked in pointed texts with a dot. The Samaritan tradition arrives at a different result by a different route, and the Samaritan script has no dot to mark anything with. The letter is written one way and read the way the community reads it.
It is also one of the five letters the square Hebrew script writes differently at the end of a word. Samaritan has no final forms at all, so this letter, like the other four, keeps one shape in every position.
Greek took the sign as pi, keeping the p and the seventeenth place, and Latin took it as P. The Latin letter F comes from somewhere else entirely, from the sixth sign by way of Greek digamma, so the resemblance between the Samaritan name Fi and the Latin letter F is a coincidence of two separate sound histories rather than a relationship between the letters.
The character is encoded at U+0810.