Forgetting is always the hard part in the journey of forgiving, and you're right that it's not a requirement to forget in order to forgive. I personally tend to forgive after processing the situation in a relatively short amount of time, don't want to live in a reality where people are given the power to make me some feel some type of way, whether that be intentionally or unintentionally.
Así mi es amigo, el perdón es un recorrido personal donde se elige desde el amor propio