Alison wrote:

: Who does the cat belong too? If it's not a stray or unwanted it's
: best to feed her.

The OP clearly meant that she feeds this cat regularly but on that one
occasion wasn't sure if it was good for the cat's health to eat right
after vomiting, so didn't feed that one time.

I am inexperienced myself, but reading the follow-up responses I
understand it is ok for cats to eat after they vomits.

Kind of counter-intuitive to me---I wouldn't hand over a full dinner
plate to my child right after he vomited---but cats do have a different
physiology from ours.