Is it possible to get sick after you've just gotten sick and given it to your dad?

I was sick with a sore throat and minor fever a few days ago, and am still getting over the remnants of it. My dad all of a sudden got a sore throat and a 102 fever, so I'm definitely uming he got it from me, considering he ate my leftovers while I was sick. I hear that viruses mutate constantly, so it's hard to get totally immune to them. Is it possible for my dad to p over the same virus to me while I'm recovering or have just recovered from it? Could the virus have mutated from the time it was in me to the time it was in my dad?