Wouldn't it be better to speak to someone personally at least over the phone?
It is hard to show emotion in written form unless you are a professional writer, besides it might be deemed as a cop out (no pun intended). If you do it in person, face to face it shows your true feelings, and intent to make things right. A cold and impersonal letter has a greater chance of receiving a cold an impersonal You're Fired" response in my book.
I had a officer that I assigned a brand new fully equipped patrol car to. It had 16 miles on the odometer when he ran code to a none code call. He went to turn on loose gravel on a blacktop road lost control and hit a huge steel Concrete filled pipe that a citizen was using for a main gatepost and totaled the car! He sent me a memo! It was compounded when I walked up behind him in the squad room unbeknownst to him while he was joking about the $40K car he trashed! Let's just say it wasn't a pleasent experience on his part! I heard he is doing well as the night desk clerk at a local motel!
Take responsibility for your actions both good and bad and people will think a lot more of you!
As others said ... You need to go speak to them in person.
And if *I* were in the HR department - I would be asking how you lost the SIM card, but not the phone? Why did you take it out of the phone, or have the phone open in the first place? Basically, you can expect to be told you destroyed company property.