If you have received an apology letter from someone, it is considered to be common courtesy that you reply to them. Make sure that you sound formal throughout the letter and explain to them how you have forgiven them.
Sample of Apology Acceptance Letter
Number 4 Private Drive
09234 Ontario, CA
How are you? I received your letter where you wanted to apologize to me regarding the little miscommunication that the two of us had and we had to fight about it.
There are absolutely no grudges that I keep against you. The two of us have been friends for the past eight years. I don’t think that an issue such small as this can cause a problem between the two of us. I understand that you thought that maybe I was angry at the fact that you told Roxana about me not being able to make it on time in the party but I must assure you that even if you did, it is totally okay and I personally believe that the whole meeting went down in my favour.
I spoke to Charles regarding the whole problem as well. He personally knows Roxana and approved that she approached him during the office party. Once again, I assure that there were no grudges that I kept for you. You sending an apology letter shouldn’t have been considered. However, thank you for accepting the fact that you thought it was wrong of you. Few people would accept their mistakes and you are one of them.
The apology letter that you sent me testifies that the two of us can’t keep any secrets. I like how you have always been honest to me and hope that this continues for years to come.
Thank you, again, for accepting that I must know the truth.