Is it true that in foreign words they use “フ” for “h” in katakana, when the h is not followed by a vocal?

I was kinda curious and used Chat GTP in turkish to let it write a name in katakana. I simply wrote “how would that name be witten in japanese?” and the first syllable ends with an H which is actually pronounced like an H. Chat GTP used フ for the H and I asked back why it used the katakana Fu for H? The answer was that it is common to use it like this because there is no H like this in katakana.

In the past I mainly saw katakana variations of that name with completely ignoring the “H” or using the katakana “HA”

Is Fu in that case indeed the better and more correct way to write it?

Thanks

by gasperoni66