write a heartfelt apology for having lost the priced possession of a dear friend.
user
Dear [Name],

I’m so sorry about my thoughtless negligence and I apologize unconditionally for my failure by losing your [item].  I have caused you needless hurt by my carelessness, and I deeply regret my actions.  You trusted me with your possession and I broke your trust.   I have considered how instead of paying attention and being diligent in safeguarding your goods, I let you down through my own absent-mindedness.  That was wrong of me, and it’s inexcusable.  I wish to replace the item to atone for my shortcoming to prove I am coming from a position of genuine remorse and goodwill.  Moving forward, I promise to be respectful to you and what is precious to you.  You mean so much to me as a friend and I never would wish to lose something important to you, and our friendship means everything to me. I would love to pick up this matter when we see each other again so I can make things right.
assistant
The language is overly formal and flowery. Make it more sincere and less repetitive.
user
Dear [Name],

I'm so sorry for losing your [item]. I know how much it meant to you and I feel terrible for letting you down. My carelessness was inexcusable and I want to apologize from the bottom of my heart.
I understand that this must have caused you a lot of pain and inconvenience, and I want to do everything I can to make it right. I would like to replace the item as a gesture of my sincere regret and to show you that I am committed to making things better.
I value our friendship deeply and I never want to do anything to jeopardize it. Losing your [item] was a huge mistake and I promise to be more careful and respectful of your belongings in the future. I hope that we can put this behind us and move forward.
Once again, I am truly sorry for what happened and I hope that you can find it in your heart to forgive me. Please let me know if there's anything else I can do to make things right.
assistant