lots of Hindi speakers will say फ as either a p(h) sound or an f sound. It varies a bit by dialect, and also with some words it's more predictable than others. Words of Persian or Arabic origin like सिर्फ ('only') are pretty consistently pronounced with an F sound, but other words like फूल ('flower') are less predictable.
Often when it's supposed to be F it will be written with a dot like फ़, but you can't always depend on that in most writing.
It depends on what language you're coming from and going to and what each one considers discrete sounds versus allophones, but there are several common patterns you can see between many languages that had contact, even if they weren't closely related.
P/f is a common one; compare Latin pater with German Vater (pronounced with an /f/ sound) are cognates.
S/sh is common too--I've heard Sri and Shri Lanka, or Sriracha and Shriracha.
So, pusa/fusa/pusha/fusha makes sense.
Also common are unvocalized+ /vocalized pairs, like t/d (think of English doublets like burnt and burned) s and z , f and v, etc.
All the relations in Hindi in this link