The Japanese consonant in "fu" (ふ) is called a voiceless bilabial fricative, represented as a ɸ. Think of ɸ as making an English F sound without using your teeth, and purely with your lips. Because the consonant sounds for "f" and "h" in Japanese are definitely different, the "hu" sound is viable, but simply doesn't exist because of how native speakers actually speak. Simply put, the vowel that the consonant is directly attached to affects how the consonant is said because the lips are shaped in the form of the vowel before the consonant is said.
I've been using ほぅ to describe "hu" when I record, although it's only really needed for CVVC and the like (VCCV, CVVCV, etc.).
(sorry for ranting about my theories about language, the subject is sort of my savvy)